Question

Найдите производную. Срочно!

Answer 1

$1.; ; y=sqrt{sinx}\\y'=frac{1}{2sqrt{sinx}}cdot cosx\\2.; ; y=(3x-6)^7\\y'=7(3x-6)^6cdot 3=21(3x-6)^6\\3.; ; y=(sqrt{x}-frac{3}{x^2})^{10}\\y'=10(sqrt{x}-frac{3}{x^2})^9cdot (frac{1}{2sqrt{x} }+frac{3cdot 2x}{x^4})=10(sqrt{x}-frac{3}{x^2})^9cdot (frac{1}{2sqrt{x}}+frac{6}{x^3})\\4.; ; y=frac{4}{(x^2-6)^4}\\y'=-frac{4cdot 4(x^2-6)^3cdot 2x}{(x^2-6)^8}=-frac{32x}{(x^2-6)^5}$

$5.; ; y=sqrt{4x^2+5}\\y=frac{1}{2sqrt{4x^2+5}}cdot 8x=frac{4x}{sqrt{4x^2+5}}\\6.; ; y=sin^2frac{x}{4}\\y'=2sinfrac{x}{4}cdot cosfrac{x}{4}cdot frac{1}{4}=frac{1}{4}cdot sinfrac{x}{2}\\7.; ; y=sqrt{cosx}\\y'=frac{1}{2sqrt{cosx}}cdot (-sinx)=-frac{sinx}{2sqrt{cosx} }$