Question

Помогите с производными

Answer 1

$(x^{n})'=ncdot x^{n-1}\\(frac{x}{4})'=(frac{1}{4}cdot x)'=frac{1}{4}\\(frac{1}{x^{11}})'=(x^{-11})'=-11cdot x^{-12}=-frac{11}{x^{12}}\\(x^{12})'=12cdot x^{11}\\(sqrt{x})'=(x^frac{1}{2})'=frac{1}{2}cdot x^{-frac{1}{2}}=frac{1}{2sqrt{x}}\\(frac{1}{sqrt{x}})'=(x^{-frac{1}{2}})'=-frac{1}{2}cdot x^{-frac{3}{2}}=-frac{1}{2sqrt{x^3}}\\(x^{-6})'=-6cdot x^{-7}=-frac{6}{x^7}\\(frac{1}{sqrt[5]{x}})'=(x^{-frac{1}{5}})'=-frac{1}{5}cdot x^{-frac{6}{5}}=-frac{1}{5sqrt[5]{x^6}}$

$(sqrt[5]{x})'=(x^{frac{1}{5} })'=frac{1}{5}cdot x^{-frac{4}{5} }=frac{1}{5sqrt[5]{x^4}}\\(sqrt3)'=0; ; ,; ; t.k.; ; sqrt3=const\\(3-2x)'=3'-(2x)'=0-2cdot x'=-2cdot 1=-2\\(frac{1}{sqrt[6]{x^2}})'=(x^{frac{2}{6}})'=(x^{frac{1}{3}})'=frac{1}{3}cdot x^{-frac{2}{3}}=frac{1}{3sqrt[3]{x^2}}$