`f(x) = sin(ln x)` Differentiate the function.

Textbook Question

Chapter 3, 3.6 - Problem 3 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to differentiate the function with respect to x, using the chain rule, such that:

`y' = (sin(ln x))'`

`y' = sin'(ln x)*(ln x)'*(x)'`

`y' =cos(ln x)*(1/x)*1`

`y' = (cos(ln x))/x`

Hence, evaluating the derivative of the given function, yields `y' = (cos(ln x))/x.`

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kalau | (Level 2) Adjunct Educator

Posted on

  Differentiate the function.

In order to differentiate this, we need to consider that there is an inner function inside sin(x).

This will require chain rule. 

The derivative involving chain rule is:

Take the derivative.

`d f(x) /dx = cos(ln(x)) * (1/x)`

The answer is:  `cos(ln(x))/x`

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