Question

What is the derivative of `sin^2(lnx)`?

Answer 1

`f(x)=sin^2(lnx) = (sin(lnx))^2`

To find `f'(x)`, use the chain rule, twice.

`f'(x)=2(sin(lnx))*[cos(lnx)*1/x]`

(The factor in the brackets is the derivative of `sin(lnx)`)

Clean up the answer however you want.

`f'(x)=2/ x sin(lnx)cos(lnx) 1/x sin(2lnx) = 1/x sin(lnx^2)`