Question

найти производные данных функций

Answer 1

Ответ:

Пошаговое объяснение:

a)

$\displaystyle y' = \bigg (x^2+x*arcsin(x)+\sqrt{1-x^2} \bigg )' =$

$\displaystyle =2x +(x'arcsinx+x(arcsinx)')+\frac{2x}{2\sqrt{1-x^2} } =$

$\displaystyle = 2x +arcsinx +\frac{x}{\sqrt{1+x^2} } +\frac{x}{\sqrt{1-x^2} }$

б)

$\displaystyle y' = \bigg ( 2 ^{ \displaystyle arcsin(1/x)} \bigg )'= 2 ^{ \displaystyle arcsin(1/x)}*ln(2)*\bigg (arcsin(1/x)\bigg )'*\bigg (\frac{1}{x} \bigg )'=$

$\displaystyle =2^{ \displaystyle arcsin(1/x)} ln(2)* \bigg (-\frac{1}{\sqrt{1-(1/x)^2} } \bigg )*\frac{1}{x^2} =-\frac{ 2^{ \displaystyle arcsin(1/x)} ln(2) }{x^2\sqrt{1-(1/x)^2} }$

в)

$\displaystyle \frac{\delta y}{\delta x} = - \frac{F'_x}{F'_y}$

$\displaystyle F'_x = -y*sin(xy)-2; \qquad F'_y = -x*sin(xy)$

$\displaystyle \frac{\delta y}{\delta x} =-\frac{y*sin(xy)-2}{x*sin(xy)}$