Question

Differentiate

$\frac{2}{3}{x}^3+\frac{3}{2}{x}^2+C$

Answer 1

Let $y=\frac{2}{3}{x}^3+\frac{3}{2}{x}^2+C$

$\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$

$\therefore \frac{dy}{dx}=\frac{d}{dx}\left(\frac{2}{3}{x}^3\right)+\frac{d}{dx}\left(\frac{3}{2}{x}^2\right)+0$ ($\because C$ is constant )

$=\frac{2}{3}.3x^2+\frac{3}{2}.2x$

$\therefore \frac{dy}{dx}=2x^2+3x$