Question

Differentiate

$3x^{1/3}+\frac{6}{7}{x}^{7/6}+3x^{2/3}+C$

Answer 1

Let $y=3x^{1/3}+\frac{6}{7}{x}^{7/6}+3x^{2/3}+C$

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

$\therefore \frac{dy}{dx}=\frac{d}{dx}\left(3x^{1/3}\right)+\frac{d}{dx}\left(\frac{6}{7}{x}^{7/6}\right)+\frac{d}{dx}\left(3x^{2/3}\right)+0$ ($\because C$ is constant)

$=3.\frac{1}{3}{x}^{-2/3}+\frac{6}{7}.\frac{7}{6}{x}^{1/6}+3.\frac{2}{3}{x}^{-1/3}$

$\therefore \frac{dy}{dx}=x^{-2/3}+x^{1/6}+2x^{-1/3}$