Question

How do you find the derivative of `(sin x)^cos x`?

Answer 1

We have `f(x)=sinx^cosx` we can write this using logarithms as

`f(x)=e^(cosx*lnsinx)`

hence its first derivative is

`(df(x))/dx=e^(cosx*lnsinx)*[(-sinx)*lnsinx+cosx*(cosx)/(sinx)]`

or

`(df(x))/dx=sinx^cosx*[cos^2x/sinx-sinx*lnsinx]`