qual a deriva de x^3/4?

0.75*x^(-0.25)

Para encontrarmos a derivada das função dada, realizaremos os cálculos abaixo:

\(\begin{align} & f(x)=\frac{{{x}^{3}}}{4} \\ & \\ & \frac{df}{dx}{{x}^{n}}=n{{x}^{n-1}} \\ & \\ & \frac{df}{dx}\left( \frac{{{x}^{3}}}{4} \right)=\frac{{{x}^{3}}}{4} \\ & \frac{df}{dx}\left( \frac{{{x}^{3}}}{4} \right)=3\cdot \frac{{{x}^{3-1}}}{4} \\ & \frac{df}{dx}\left( \frac{{{x}^{3}}}{4} \right)=3\cdot \frac{{{x}^{2}}}{4} \\ & \frac{df}{dx}\left( \frac{{{x}^{3}}}{4} \right)=\frac{3{{x}^{2}}}{4} \\ \end{align}\ \)

Portanto, a derivada da função dada será:

\(\begin{align} & \frac{df}{dx}\left( \frac{{{x}^{3}}}{4} \right)=\frac{3{{x}^{2}}}{4} \\ \end{align}\ \)