Question

Assinale a alternativa que contém a derivada da função $f(x)=1/4\sqrt[4]{x^3}+1/3\sqrt[3]{x^2}$

Answer 1

$\boxed{\begin{array}{l}\sf f(x)=\dfrac{1}{4\sqrt[\sf4]{\sf x^3}}+\dfrac{1}{3\sqrt[\sf3]{\sf x^2}}\\\\\sf f(x)=\dfrac{1}{4}x^{-\frac{3}{4}}+\dfrac{1}{3}x^{-\frac{2}{3}}\\\\\sf f'(x)=\dfrac{1}{4}\cdot-\dfrac{3}{4}x^{-\frac{3}{4}-1}+\dfrac{1}{3}\cdot-\dfrac{2}{3}x^{-\frac{2}{3}-1}\\\\\sf f'(x)=-\dfrac{3}{16}x^{-\frac{7}{4}}-\dfrac{2}{9}x^{-\frac{5}{3}}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf f'(x)=-\dfrac{3}{16\sqrt[\sf4]{\sf x^7}}-\dfrac{2}{9\sqrt[\sf3]{\sf x^5}}}}}}\end{array}}$