Question

The derivative of $\frac{d}{dx}\left(\frac{1}{x\sqrt{x}}\right)=$ .

• A. $\frac{2}{3x^{3/2}}$
• B. $\frac{-3}{2x^{5/2}}$
• C. $x^{-5/2}$
• D. $x^{5/2}$

Answer 1

The correct option is B $\frac{-3}{2x^{5/2}}$

The derivative of a function of the form of $x^n=n{x}^{n-1}.$
Now $\frac{1}{x\sqrt{x}}=\frac{1}{x^{3/2}}=x^{-3/2}.$
$\frac{d}{dx}\left(x^{-3/2}\right)=\frac{-3}{2}{x}^{(-3/2-1)}$

$=\frac{-3}{2}{x}^{-5/2}$ or $\frac{-3}{2x^{5/2}}$, which is the correct answer.