Find f ' in terms of g '. f(x) = x^2g(x) ?

Question

Find f ' in terms of g '. f(x) = x^2g(x) ?

Answer 1

f(x) = x^2g(x)

Need to use product rule.

f'(x)=2xg(x)+x^2g'(x)

Answer 2

usually when you have a variable raised to another variable, you take the natural logs of both sides to get:

ln f = 2g ln x

differentiate:

d/dx (ln f) = df/dx/f = 2g' ln x + 2g/x

or f'/f = 2g' lnx +2g/x

f'=2g' f lnx + 2gf/x