Question

Найти похідну функції

Answer 1

Ответ:

$896)\ \ \ y=x^2\sqrt{1-x^2}\\\\y'=2x\cdot \sqrt{1-x^2}+x^2\cdot \dfrac{-2x}{2\sqrt{1-x^2}}=2x\cdot \sqrt{1-x^2}-\dfrac{x^3}{2\sqrt{1-x^2}}=\\\\\\=\dfrac{4x(1-x^2)-x^3}{2\sqrt{1-x^2}}=\dfrac{4x-5x^3}{2\sqrt{1-x^2}}$

$898)\ \ \ y=\sqrt[3]{1+cos6x}=(1+cos6x)^{\frac{1}{3}}\\\\\\y'=\dfrac{1}{3}\cdot (1+cos6x)^{-\frac{2}{3}}\cdot (-6sin6x)=-\dfrac{2sin6x}{\sqrt[3]{(1+cos6x)^2}}$