Question

qual a derivada de f(x)1/3X^3+0,75x^2-raiz de5

Answer 1

$\displaystyle f(x)=\frac{1}{3}x^3+0.75x^2-\sqrt{5}$

derivada das somas é igual à soma das derivadas:
$\displaystyle \frac{df}{dx}=\frac{d}{dx}\left(\frac{1}{3}x^3\right)+\frac{d}{dx}(0.75x^2)-\frac{d}{dx}\sqrt{5}$

derivada de polinômio:
regra do expoente:
$\displaystyle \frac{d}{dx}x^n=n\cdot x^{n-1}$

então:
$\displaystyle i)~~~\frac{d}{dx}\left(\frac{1}{3}x^3\right)=x^2\\\\ii)~~\frac{d}{dx}(0.75x^2)=2\cdot(0.75x)=1.5x\\\\iii)~\frac{d}{dx}\sqrt{5}=0$
a derivada da função é:
$\boxed{ \frac{df}{dx}=x^2+0.75x}$