Question

Найдите производную функции​

Answer 1

Ответ:

$1)\ \ y=\dfrac{3}{x}+\sqrt[5]{x^7}-4x^6+\dfrac{2}{x^5}\\\\y'=-\dfrac{3}{x^2}+\dfrac{7}{5}\, \sqrt[5]{x^2} -24x^5-\dfrac{10}{x^4}\\\\\\2)\ \ y=sin(3x^2-2x+1)\\\\y'=cos(3x^2-2x+1)\cdot (6x-2)\\\\\\3)\ \ y=\sqrt[3]{(arccos\, 4x+5)^2}\\\\\displaystyle y'=\frac{2}{3}\cdot (arccos\, 4x+5)^{-\frac{1}{3}}\cdot \frac{-4}{\sqrt{1-16x^2}}=-\frac{8}{3\sqrt[3]{arccos\, 4x+5}}\cdot \frac{1}{\sqrt{1-16x^2}}$

$4)\ \ y=cos^72x\cdot arctg3x^3\\\\y'=7cos^62x\cdot (-2sin2x)\cdot arctg(3x^3)+cos^72x\cdot \dfrac{1}{1+9x^6}\cdot 9x^2$