Question

3. Calcule a derivada das funções definidas a seguir:

a) f(x) = ∛ ($x^{2}$ + 1)²

Answer 1

$\\f(x)=\sqrt[3]{(x^2+1)^2}\\\\f(x)=(x^2+1)^{\frac{2}{3}}\\\\f'(x)=\frac{2}{3}\cdot(x^2+1)^{\frac{2}{3}-1}\cdot2x\\\\f'(x)=\frac{4x}{3}\cdot(x^2+1)^{-\frac{1}{3}}\\\\f'(x)=\frac{4x}{3}\cdot\frac{1}{(x^2+1)^{\frac{1}{3}}}\\\\\boxed{f'(x)=\frac{4x}{3\sqrt[3]{x^2+1}}}$