Question

f(x)=ln^3x+2/x -1, помогите пожалуйста.

Answer 1

$f(x)=\frac{ln^3x+2}{x-1} \\\\f'(x)= \frac{3ln^2x\cdot \frac{1}{x}(x-1)-(ln^3x+2)\cdot 1}{(x-1)^2}=\frac{3ln^2x\cdot (1-\frac{1}{x})-ln^3x-2}{(x-1)^2}\\\\f'(e)=\frac{3(1-\frac{1}{e})-1-2}{(e-1)^2}= \frac{3- \frac{1}{e}-3}{(e-1)^2}=-\frac{1}{e\cdot (e-1)^2}$