Question

Determine f′(x) for f(x)=(ln(3x))^9.

Answer 1

in other words find dy/dx for f(x)=(ln(3x))^9.

Answer 2

Do the chain rule.
f(x)=g(h(x))
f'(x) = g'(h(x))*h'(x)

if your f(x) = (ln(x^2))^2
your h(x)=ln(x^2)
your g(x)= (h(x))^2
f'(x) in this case = \[2*(ln(x^2))*\frac{1}{ln(x^2)}*2x\]
In this case, I had to do the chain rule twice. Notice the x^2 in the ln(x^2) had to be differentiated as well.