Question

Помогите !!!Производная с решением

Answer 1

$1)\quad y=8x^2+\sqrt[3]{x^4}- \frac{4}{x} - \frac{2}{x^3} \\\\y'=16x+\frac{4}{3}\cdot x^{\frac{1}{3}}-\frac{-4}{x^2}- \frac{-2\cdot 3x^2}{x^6} =16x+ \frac{4}{3} \cdot \sqrt[3]{x}+ \frac{4}{x^2} +\frac{6}{x^4} \\\\2)\quad y=2cosx\cdot arcctg(5x^3)\\\\y'=-2sinx\cdit arcctg(5x^3)+2cosx\cdot \frac{-1}{1+(5x^3)^2} \cdot 15x^2\\\\3)\quad y= \frac{3}{(x-4)^7} + \sqrt{5x^2-4x+3}\\\\y'= 3\cdot (-7)\cdot (x-4)^{-8}+\frac{1}{2\sqrt{5x^2-4x+3}} \cdot (10x-4)=\\\\=-\frac{21}{(x-4)^8}+\frac{5x-2}{\sqrt{5x^2-4x+3}}$

$4)\quad y= -x\cdot arcsin^25x\\\\y'=-arcsin^25x-x\cdot 2arcsin(5x)\cdot \frac{1}{\sqrt{1-(5x)^2}} \cdot 5=\\\\=-arcsin^25x- \frac{10x\cdot arcsin(5x)}{\sqrt{1-25x^2}}$