Question

If $y=x^2+5x^{\frac{3}{2}}+\frac{2}{x},then\frac{dy}{dx}=$

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is D

none of these

Differentiating both sides w.r.t. 'x'
$\frac{dy}{dx}=\frac{d}{dx}[x^2+5x^{\frac{3}{2}}+\frac{2}{x}]$
Using the linearity property of the differentiation, we get = $\frac{d}{dx}\left[x^2\right]+\frac{d}{dx}\left[5x^{\frac{3}{2}}\right]+\frac{d}{dx}\left[\frac{2}{x}\right]$
Taking constants out, = $\frac{d}{dx}\left[x^2\right]+5\frac{d\left[x^{\frac{3}{2}}\right]}{dx}+2\frac{d}{dx}\left[\frac{1}{x}\right]$
=$2x+5.\frac{3}{2}{x}^{\frac{1}{2}}+2.(-1)x^{-2}=2x+\frac{15}{2}{x}^{\frac{1}{2}}-\frac{2}{x^2}$