# y = 2^sin(pi x) Find the derivative of the function.

### Textbook Question

Chapter 3, 3.4 - Problem 33 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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growley52 | College Teacher | (Level 1) Adjunct Educator

Posted on

Let

u = sin(pi*x)

y = 2^(u), (dy)/(du) = 2^(u)log2

(du)/(dx) = cos(pi*x) * pi

and y' = pi*log(2)*2^(sin(pi*x))*cos(pi*x)

akbansa1506 | High School Teacher | eNotes Newbie

Posted on

Take log on both side,we get

log y = Sin(

dy/ydx=  Cos( )log2

dy/dx= y  Cos(\pi x )log2

dy/dx=

akbansa1506 | High School Teacher | eNotes Newbie

Posted on

Take log on both side,we get

log y = Sin(pix) log2

dy/ydx= pi Cos(pix )log2

dy/dx= y  Cos(  )log2

dy/dx=2^{\sin(\pi x)}.\pi .log2.Cos(\pi x)



vineetchaurasia | (Level 1) eNoter

Posted on

It is a simple question of derivation where the derivative can be find out by using substitution. The detailed solution is given the image uploaded. Please refer to it.

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