Question

qual é derivada de f(x) raiz3(x^3-×^2)

Answer 1

Olá

F(x)=$\sqrt[3]{x^3-x^2}$


$Pela~regra~de~cadeia \\ \\ \frac{df}{dx} = \frac{df}{du} .\frac{du}{dx} \\ \\ \frac{df}{dx}= \frac{d}{du} \sqrt{u}. \frac{d}{dx }(x^3-x^2) \\ \\ Derivando \\ \\ \frac{d}{du} \sqrt{u}= \frac{1}{3}u^ \frac{1}{3}^-^1 = \frac{1}{3 \sqrt[3]{(u)^2} } \\ \\ \frac{d}{dx}(x^3-x^2)=3x^2-2x \\ \\ \frac{df}{dx}= \frac{1}{3 \sqrt[3]{u} }.3x^2 -2x \\ \\ \frac{df}{dx}= \frac{3x^2-2x}{3 \sqrt[3]{(x^3-x^2)^2} }$