Question

What is `f'(x)` if `f(x)=sin((cosx)/x)`?

Answer 1

`f'(x) = -(xsinx+cosx)/x^2*cos(cosx/x)`

Explanation:

`f(x) = sin(cosx/x)`

By the chain rule, `f'(x) = (cosx/x)^' *cos(cosx/x)`

Use the quotient rule to find `(cosx/x)^'`:

`(cosx/x)^' = ((-sinx)x-(1)cosx)/x^2= -(xsinx+cosx)/x^2`

`therefore f'(x) = -(xsinx+cosx)/x^2*cos(cosx/x)`