Question

Please just tell me the formula for d/dx f(x)^g(x). I think it's something like f(x)^g(x) * g'(x) * ln(f(x)), but the internet just won't give me a straight answer.

Answer 1

d/dx( f(x)^g(x) ) = f(x)^g(x) * d/dx( g(x) ) * ln( f(x) )
+ f(x)^( g(x)-1 ) * g(x) * d/dx( f(x) )

Answer 2

http://mathforum.org/library/drmath/view/53679.html

Answer 3

That's much longer than I remember, but thanks

Answer 4

ok, let \(h= f^g\), then \(lnh = glnf\)
Take derivative both sides, you have \(\dfrac{h'}{h}=g'lnf +f'(g/f)\)
hence \(h'= h*RHS\)
but h' = (f^g)'
just replace back