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

Expert Answers
kalau eNotes educator| Certified Educator

  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`

sciencesolve eNotes educator| Certified Educator

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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