Question

Срочно!!! Найти производные функций

Answer 1

$1); ; y=6x^2-frac{5}{x^2}-sqrt[3]{x^2}\y'=12x-5cdot frac{-2}{x^3}-frac{2}{3}cdot x^{-frac{1}{3}}\\2); ; y=5^{x}(x^5-10x)\y'=5^{x}, ln5(x^5-10x)+5^{x}cdot (5x^4-10)\\3); ; y=8^{4x}cdot sqrt {e^{x}}\y'=8^{4x}cdot 4ln8cdot sqrt{e^{x}}+8^{4x}cdot frac{1}{2sqrt{e^{x}}}cdot e^{x}\\4); ; y=frac{5x^2}{x-3}\y'=frac{10x(x-3)-5x^2cdot 1}{(x-3)^2}=frac{5x^2-30x}{(x-3)^2}=frac{5x(x-6)}{(x-3)^2}\\5); ; y=lnsqrt[6]{cosx}\y'=frac{1}{sqrt[6]{cosx}}cdot frac{1}{6}cdot (cosx)^{-frac{5}{6}}cdot (-sinx)$

$6); ; y=cos^4xcdot 2, lnx\y'=4cos^3xcdot (-sinx)cdot 2, lnx+cos^4xcdot frac{2}{x}\\7); ; y=arccosfrac{1-sqrt{x}}{1+sqrt{x}}\\y'=frac{-1}{sqrt{1-(frac{1-sqrt{x}}{1+sqrt{x}}})^2}}cdot frac{-frac{1}{2sqrt{x}}cdot (1+sqrt{x})-(1-sqrt{x})cdot frac{1}{2sqrt{x}}}{(1+sqrt{x})^2}=\\=-frac{1+sqrt{x}}{sqrt{(1+sqrt{x})^2-(1-sqrt{x})^2}}cdot frac{-1-sqrt{x}-1+sqrt{x}}{2sqrt{x}(1+sqrt{x})^2}=frac{1}{2sqrt[4]{x^3}cdot (1+sqrt{x})}$