Question

$\frac{d}{dx}\left(\frac{1}{x\sqrt{x}}\right)=$

• A. $\frac{-3}{2}{x}^{-3/2}$
• B. $\frac{-3}{2}{x}^{-5/2}$
• C. $x^{-5/2}$
• D. None of the above

Answer 1

The correct option is B

$\frac{-3}{2}{x}^{-5/2}$

As mentioned in the videos that derivative of a function in the form of $x^n=n{x}^{n-1}.$
Now looking at this function closely we can say that it is nothing but $\frac{1}{x^{1+1/2}}=\frac{1}{x^{3/2}}=x^{-3/2}.$
So, $\frac{d}{dx}\left(x^{-3/2}\right)=\frac{-3}{2}{x}^{(-3/2-1)}$(Using the above mentioned formula).
$=\frac{-3}{2}{x}^{-5/2}$, which is the correct answer.