What is derivative of $sin ax$ where $a$ is a constant?











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What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







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  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 at 15:17















up vote
1
down vote

favorite












What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question









New contributor




Chaku Daku is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 at 15:17













up vote
1
down vote

favorite









up vote
1
down vote

favorite











What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question









New contributor




Chaku Daku is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential




calculus algebra-precalculus derivatives differential






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Chaku Daku is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Nov 29 at 19:19









Asaf Karagila♦

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asked Nov 29 at 15:17









Chaku Daku

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  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 at 15:17














  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 at 15:17








1




1




Apply the chain rule.
– user3482749
Nov 29 at 15:17




Apply the chain rule.
– user3482749
Nov 29 at 15:17










3 Answers
3






active

oldest

votes

















up vote
6
down vote













HINT



Recall that by chain rule



$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






share|cite|improve this answer




























    up vote
    3
    down vote













    begin{array}{c}
    frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
    = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
    = left( {cos ax} right) cdot a cdot 1\
    = aleft( {cos ax} right)
    end{array}






    share|cite|improve this answer

















    • 1




      Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
      – Chris
      Nov 29 at 17:20






    • 1




      @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
      – Paul Sinclair
      Nov 29 at 17:29


















    up vote
    1
    down vote













    Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      6
      down vote













      HINT



      Recall that by chain rule



      $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






      share|cite|improve this answer

























        up vote
        6
        down vote













        HINT



        Recall that by chain rule



        $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






        share|cite|improve this answer























          up vote
          6
          down vote










          up vote
          6
          down vote









          HINT



          Recall that by chain rule



          $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






          share|cite|improve this answer












          HINT



          Recall that by chain rule



          $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 29 at 15:20









          gimusi

          89.4k74495




          89.4k74495






















              up vote
              3
              down vote













              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer

















              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 at 17:29















              up vote
              3
              down vote













              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer

















              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 at 17:29













              up vote
              3
              down vote










              up vote
              3
              down vote









              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer












              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Nov 29 at 16:10









              Krishna Srivastav

              894




              894








              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 at 17:29














              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 at 17:29








              1




              1




              Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
              – Chris
              Nov 29 at 17:20




              Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
              – Chris
              Nov 29 at 17:20




              1




              1




              @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
              – Paul Sinclair
              Nov 29 at 17:29




              @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
              – Paul Sinclair
              Nov 29 at 17:29










              up vote
              1
              down vote













              Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






              share|cite|improve this answer










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              Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                up vote
                1
                down vote













                Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






                share|cite|improve this answer










                New contributor




                Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.




















                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






                  share|cite|improve this answer










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                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.







                  share|cite|improve this answer










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                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Nov 29 at 15:42









                  Tianlalu

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                  2,8811935






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                  answered Nov 29 at 15:21









                  Rohit Bharadwaj

                  518




                  518




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                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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