Question

What is the derivative of `y=(lnx)^(cosx)`?

Answer 1

Use substitution

Explanation:

`ln y = cos x ln(ln(x))`
`1/y dy/dx = sin x ln(ln x)+cosx 1/ln(x) 1/x`
`dy/dx = (ln x)^(cos x)\times (sin x ln(ln x)+cosx 1/ln(x) 1/x)`