Question

What is the derivative of `(ln x) ^ cos x`?

Answer 1

`(lnx)^cosx ( -sinx ln lnx + cosx /(x lnx))`

Explanation:

Let `y=(ln x)^cos x`, so that ln y= cos x ln ln x

Now differentiate both sides,

`1/y dy/dx = -sinx ln ln x + cos x 1/lnx 1/x`

`dy/dx= (lnx)^cosx ( -sinx ln lnx + cosx /(x lnx))`