If f(x)= (3x)^(3x), then f'(x) = ?

Question

Thank you!

Answer 1

let y = (3x)^(3x)
take ln of both sides

ln y = ln (3x)^(3x)
ln y = 3x ln 3x

(dy/dx) / y = 3x(1/x) + 3ln(3x)
dy/dx = (3 + 3ln(3x)) (3x)^(3x)