Question

função derivada de f(x)= 8^(-3) * x^(-2/3)

Answer 1

$\frac{df}{dx}=\frac{du}{dx}.v+\frac{dv}{dx}.u \\u=8^{-3}\\v=x^{-\frac{2}{3}} \\\frac{du}{dx}=0 \\\frac{dv}{dx}=-\frac{2}{3}.x^{(-\frac{2}{3}-1)=-\frac{2x^{-\frac{5}{3}}}{3}=-\frac{2}{3\sqrt[3]{x^5}}$

$\frac{df}{dx}=0+(-\frac{2}{3\sqrt[3]{x^5}}.\frac{1}{8^3})=-\frac{2}{3.8^3\sqrt[3]{x^5}}=-\frac{2}{1536\sqrt[3]{x^5}}=\underbrace{-\frac{1}{768\sqrt[3]{x^5}}}$