Question

Calcule o valor da derivada f (x)= 2/3x2

Answer 1

Resolução da questão, veja:

Devemos puxar as constantes desta derivada para fora do derivado, veja:

$\mathsf{f'(x)=\dfrac{d}{dx}~\dfrac{2}{3x^{2}}}}\\\\\\\\ \mathsf{f'(x)=\dfrac{2}{3}~\cdot~\dfrac{d}{dx}~\cdot~\bigg(\dfrac{1}{x^{2}}\bigg)}}}}}\\\\\\\\\ \mathsf{f'(x)=\bigg(\dfrac{2}{3}~\dfrac{d}{dx}~(x^{-2})\bigg)}}}\\\\\\\\ \mathsf{f'(x)=\dfrac{2}{3}~\cdot~-2x^{-2-1}}\\\\\\\\ \mathsf{f'(x)=\dfrac{2}{3}~(-2x)^{-3}}}}\\\\\\\\ \mathsf{f'(x)=\dfrac{2}{3}~\cdot~(-2)~\cdot~\dfrac{1}{x^{3}}}}}}\\\\\\\\\ \mathsf{f'(x)=\dfrac{2~\cdot~(-2)~\cdot~1}{3x^{3}}}}}\\\\\\\\\ \large\boxed{\boxed{\mathsf{f'(x)=\dfrac{-4}{3x^{3}}}}}}}}}}}}}}}}}}}}}}}}}}$

Espero que te ajude. '-'