find f prime

Question

f(x)=[ln x]^7
f’(x)=
f’(e^2)=

Answer 1

f(x) = (ln x)⁷

 

To evaluate f ', use the chain rule letting u = ln x so f(u) = u⁷

 

f '(x) = df(u)/du * du/dx = d(u⁷)/du * d(ln x)/dx

 

f '(x) = 7u⁶ * (1/x) = (7/x)(ln x)⁶

 

f '(e²) = (7/e²)(ln e²)⁶ = (7*2⁶)/e² ≅ 60.63