Question

Differentiate

$2x^{3/2}+2x^{5/2}+C$

• A. $\frac{dy}{dx}=\sqrt{x}(3+5x)$
• B. $\frac{dy}{dx}=\sqrt{x}(3-5x)$
• C. $\frac{dy}{dx}=-\sqrt{x}(3+5x)$
• D. None of these

Answer 1

The correct option is A $\frac{dy}{dx}=\sqrt{x}(3+5x)$

Let $y=2x^{3/2}+2x^{5/2}+C$

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

$\therefore \frac{dy}{dx}=\frac{d}{dx}\left(2x^{3/2}\right)+\frac{d}{dx}\left(2x^{5/2}\right)$

$=2.\frac{3}{2}{x}^{1/2}+2.\frac{5}{2}{x}^{3/2}$

$\therefore \frac{dy}{dx}=\sqrt{x}(3+5x)$