Question

ПРОИЗВОДНАЯ!!!!!!!Помогите решить!

Answer 1

Ответ:

$11)\;y=(x+1)^{\frac{1}{x} }\\\\lny=\frac{1}{x}ln(x+1)\\\frac{y'}{y} =-\frac{1}{x^2}*ln(x+1)+\frac{1}{x}*\frac{1}{x+1} \\y'=(-\frac{ln(x+1)}{x^2}+\frac{1}{x(x+1)})*(x+1)^{\frac{1}{x} }$

$12)\;\left \{ {{x=lnx} \atop {y=t^2}} \right. \\x'_t=\frac{1}{t}\\y'_t=2t\\\\y'_x=\frac{dy}{dx}=\frac{y'_t}{x'_t}=\frac{2t}{\frac{1}{t} }=2t^2\\\\(y'_x)'_t=4t\\y''_{xx}=\frac{d^2y}{dx^2}=\frac{(y'_x)'_{t}}{x'_t}=\frac{4t}{\frac{1}{t} }=4t^2$