Question

find f'(x) for f(x) = x^(x^2)

Answer 1

you have a choice although the work will be identical
either take the log, take the derivative of the log, and then multiply your answer by the original function, or else rewrite this as
\[x^{(x^2)}=e^{x^2\ln(x)}\] and take the derivative using the chain rule

Answer 2

and of course the product rule since \(x^2\ln(x)\) is a product

Answer 3

thank you much