Question

помните пожалуйста. срочно. производная​

Answer 1

$1)\; f(x)=x^6\; \; f`(\frac{1}{2})=?\\\\f`(x)=(x^6)`=6x^5\\f`(\frac{1}{2})=6(\frac{1}{2})^5 =\frac{6}{2^5}=\frac{6}{32}=\frac{3}{16} \\\\\\2)\; f(x)=\sqrt{x} \; \;\; f`(4)=?\\\\f`(x)=(\sqrt{x})`=\frac{1}{2\sqrt{x}}\\f`(4)=\frac{1}{2\sqrt{4}}=\frac{1}{2*2}=\frac{1}{4}=0,25\\\\\\3)\; f(x)=x^{-2}\; \; \; f`(3)=?\\\\f`(x)=(x^{-2})`=-2x^{-2-1}=-2x^{-3}=-\frac{2}{x^3}\\f`(3)=-\frac{2}{3^3}=-\frac{2}{27}$

$4)\; f(x)=\sqrt[3]{x}\; \; \; f`(8)=?\\\\f`(x)=(\sqrt[3]{x})`=\frac{1}{3}x^{\frac{1}{3}-1}=\frac{1}{3}x^{-\frac{2}{3}}=-\frac{1}{3\sqrt[3]{x^2}}\\f`(8)=\frac{1}{3\sqrt[3]{8^2}}=\frac{1}{3\sqrt[3]{(2^3)^2}}=\frac{1}{3\sqrt[3]{4^3}}=\frac{1}{3*4}=\frac{1}{12}$