Question

Найдите производную функции:
4*$\sqrt[3]{x}$-3*$\sqrt[4]{x}$

Answer 1

$\frac{d}{dx}(4\sqrt[3]{x}-3\sqrt[4]{x})=\\\\=\frac{d}{dx}(4\sqrt[3]{x})-\frac{d}{dx}(3\sqrt[4]{x})=\\\\=4\frac{d}{dx}(\sqrt[3]{x})-3\frac{d}{dx}(\sqrt[4]{x})=\\\\=4\frac{d}{dx}(x^{\frac{1}{3}})-3\frac{d}{dx}(x^{\frac{1}{4}})=\\\\=4\cdot \frac{1}{3}x^{\frac{1}{3}-1}-3\cdot \frac{1}{4}x^{\frac{1}{4}-1}=\\\\=4\cdot \frac{1}{3}x^{-\frac{2}{3}}-3\cdot \frac{1}{4}x^{-\frac{3}{4}}=\\\\=4\cdot \frac{1}{3}\cdot \frac{1}{x^{\frac{2}{3}}}-3\cdot \frac{1}{4}\cdot \frac{1}{x^{\frac{3}{4}}}=$

$=\frac{4}{3x^{\frac{2}{3}}} - \frac{3}{4x^{\frac{3}{4}}}$