Question

Ребят, срочно. ..............................

Answer 1

1)
$y=3x^{ \frac{3}{2} }+5* \frac{1}{x}-x^{- \frac{1}{4} }+2 \\ \\ y'=3* \frac{3}{2}x^{ \frac{3}{2}- \frac{2}{2} }-5* \frac{1}{x^2}+ \frac{1}{4}x^{- \frac{1}{4}- \frac{4}{4}} = \\ \\ =4.5 \sqrt{x} - \frac{5}{x^2}+ \frac{1}{4x \sqrt[4]{x} }$

2)
$y'=cos(x+5-x^2)*(1-2x)=(1-2x)cos(x+5-x^2)$

3)
$y'=4*(- \frac{1}{sin^2x} )*lnx+ \frac{4ctgx}{x}= \frac{4ctgx}{x}- \frac{4lnx}{sin^2x}$

4)
$y'= \frac{8x(x^2-1)-2x(4x^2+1)}{(x^2-1)^2}= \frac{8x^3-8x-8x^3-2x}{(x^2-1)^2}=- \frac{10x}{(x^2-1)^2}$

5)
$y=(sinx)^{- \frac{1}{3} } \\ \\ y'=- \frac{1}{3}(sinx)^{- \frac{1}{3}- \frac{3}{3} }*cosx=- \frac{cosx}{3sinx \sqrt[3]{sinx} }=- \frac{ctgx}{3 \sqrt[3]{sinx} }$