If y=x2+5x32+2x, then dydx= ?

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Question

If

y = x^{2} + 5 x^{\frac{3}{2}} + \frac{2}{x}, t h e n \frac{d y}{d x} =

?

Options:

A . 2x+152√x−2x2

B . 2x+103x+2lnx

C . 2x+15√x+2lnx

D . none of these

Answer: Option D
:
D
Differentiating both sides w.r.t. 'x'

\frac{d y}{d x} = \frac{d}{d x} [x^{2} + 5 x^{\frac{3}{2}} + \frac{2}{x}]

Using the linearity property of the differentiation, we get =

\frac{d}{d x} [x^{2}] + \frac{d}{d x} [5 x^{\frac{3}{2}}] + \frac{d}{d x} [\frac{2}{x}]

Taking constants out, =

\frac{d}{d x} [x^{2}] + 5 \frac{d [x^{\frac{3}{2}}]}{d x} + 2 \frac{d}{d x} [\frac{1}{x}]

=

2 x + 5. \frac{3}{2} x^{\frac{1}{2}} + 2. (- 1) x^{- 2} = 2 x + \frac{15}{2} x^{\frac{1}{2}} - \frac{2}{x^{2}}

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