Question

Find derivative of $f\left(x\right)=x^{\frac{1}{2}}+8x^{\frac{1}{3}}-\frac{1}{2}{x}^{\frac{1}{4}}$

• A. $\frac{1}{2}{x}^{-\frac{1}{2}}$+$\frac{8}{3}{x}^{-\frac{2}{3}}-\frac{1}{8}{x}^{-\frac{3}{4}}$
• B. $\frac{1}{2}{x}^{-\frac{1}{2}}$+$\frac{8}{3}{x}^{-\frac{2}{3}}-\frac{1}{8}{x}^{-\frac{5}{4}}$
• C. $\frac{3}{2}{x}^{-\frac{1}{2}}$+$\frac{8}{3}{x}^{-\frac{2}{3}}-\frac{1}{8}{x}^{-\frac{3}{4}}$
• D. $\frac{1}{2}{x}^{-\frac{1}{2}}$+$\frac{8}{3}{x}^{-\frac{4}{3}}-\frac{1}{8}{x}^{-\frac{3}{4}}$

Answer 1

The correct option is A $\frac{1}{2}{x}^{-\frac{1}{2}}$+$\frac{8}{3}{x}^{-\frac{2}{3}}-\frac{1}{8}{x}^{-\frac{3}{4}}$

Given $f\left(x\right)=x^{\frac{1}{2}}+8x^{\frac{1}{3}}-\frac{1}{2}{x}^{\frac{1}{4}}$
$\therefore \text{Derivative will be}\frac{df\left(x\right)}{dx}=\frac{d}{dx}(x^{\frac{1}{2}}+8x^{\frac{1}{3}}-\frac{1}{2}{x}^{\frac{1}{4}})$
$=\frac{d{x}^{\frac{1}{2}}}{dx}+8\frac{d{x}^{\frac{1}{3}}}{dx}-\frac{1}{2}\frac{d{x}^{\frac{1}{4}}}{dx}$
$=\frac{1}{2}{x}^{-\frac{1}{2}}$+$\frac{8}{3}{x}^{-\frac{2}{3}}-\frac{1}{8}{x}^{-\frac{3}{4}}$