`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's profile pic

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's profile pic

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's profile pic

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)`

``

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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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