SOLUTION: find the derivative of the function {{{y = 2 ^ (sin(pi*x))}}}

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Question 353582: find the derivative of the function

Found 3 solutions by vleith, Fombitz, Edwin McCravy:
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
Use this URL. Then click Show Steps to see the work
http://www.wolframalpha.com/input/?i=+y%3D2+^+%28sin+pi+x%29++derivative
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Use the chain rule,
Let



Put it all together,
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!



Take natural logs of both sides







Use a rule of logarithms of exponentials on the right side:











[I wrote it that way so your would recognize that ln(2) is just a constant.]



Find the derivative of both sides, remembering that ln(2) is just a

constant and that we must use the chain rule on the right side by

taking the derivitive of the "inside":











Multiply both sides by y







To get the derivative in terms of x only, we go back to

the original equation  and

substitute for y







Writing the constants first, and the more complicated factor last:



 

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