let f be a differentiable function. Let f(x)= [ln f(3x)]^2. then which one is f'(x)?

a) 1/[f(3x)]^2
B) 2 ln f(3x) x f'(3x)/(3x)
C) 1/f(3x)^2
D) 6 ln f(3x) x f'(3x)/f(3x)

Question

let f be a differentiable function. Let f(x)= [ln f(3x)]^2. then which one is f'(x)?

a) 1/[f(3x)]^2
B) 2 ln f(3x) x f'(3x)/(3x)
C) 1/f(3x)^2
D) 6 ln f(3x) x f'(3x)/f(3x)

anonymous · Answer

apply chain rule on the right side

anonymous · Answer

D is the best answer for this 
Solve, we have F(x) = [ln f(3x)]^2 , then 
F'(x) = 2[ln f(3x)]^{2-1} . {1/f(3x)} .f'(3x) .3 { derivative of x^2 =2x^{n-1} then we need to find the derivative of ln f(3x). 
So derivatives of ln x = 1/x, and derivatives of f(x) is f'(x) and derivatives of 3x is 3}
= 6 ln f(3x) .f'(3x) /f(3x)