Question

Dada a função:


Marque a alternativa que corresponde a derivada da função.

Answer 1

Resposta:y^ prime (x)=- 3 2 x^ - 5 2 + 4 3 x^ 1/3

Explicação passo a passo:

Answer 2

Resposta:

$\sf y(x)=x^{-\frac{3}{2}}+x^{\frac{4}{3}}$

$\sf y'(x)=\frac{d}{dx}(x^{-\frac{3}{2}}+x^{\frac{4}{3}})$

$\sf y'(x)=\frac{d}{dx}x^{-\frac{3}{2}}+\frac{d}{dx}x^{\frac{4}{3}}$

$\sf y'(x)=-\frac{3}{2}\cdot x^{-\frac{3}{2}-1}+\frac{4}{3}\cdot x^{\frac{4}{3}-1}$

$\sf y'(x)=-\frac{3}{2}\cdot x^{-\frac{5}{2}}+\frac{4}{3}\cdot x^{\frac{1}{3}}$

$\sf y'(x)=-\frac{3}{2}\cdot \frac{1}{x^{\frac{5}{2}}}+\frac{4}{3}\cdot x^{\frac{1}{3}}$

$\red{\sf y'(x)=-\frac{3}{2x^{\frac{5}{2}}}+\frac{4}{3} x^{\frac{1}{3}}}$

Regras de derivação usadas:

• $\sf\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)$

• $\sf\frac{d}{dx}x^n=n\cdot x^{n-1}$