What is f'(x) if f(x) = ln(x+1)^3?

Assuming you mean ln( (x+1)^3 )

the 3 can be brought down to the front using laws of exponents

f(x) = 3 ln(x+1)

The derivative of an Ln function is the derivative of whats inside over the original.

so if f(x) = ln ( g(x) ) then f'(x) = g'(x)/g(x)

and remember the 3 is a constant multiple so you can pull it out front while taking the derivative

so....

f'(x) = 3 (1/(x+1))

simplify

f'(x) = 3/(x+1)

F'(x) = (1/(x+1)^3)3(x+1)^2 = 3/(x+1)

f(x) = ln(x+1)³

f'(x) = ln'(x+1)³

f(x) = ln(x+1)^3

f'(x) = 3ln(x + 1)^2 d/dx 1/(x + 1) d/dx 1

......3ln^2(x + 1)

= ------------------------ answer//

.........x + 1