If y = 3 x + 2 + 1 2 x 2 + 4 , then d y d x is equal to:

Question

If $y = \sqrt{3 x + 2} + \frac{1}{\sqrt{2 x^{2} + 4}}$ , then $\frac{d y}{d x}$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{3}{2 \sqrt{3 x + 2}} - \frac{2 x}{{(2 x^{2} + 4)}^{3 / 2}}$

Explanation:

Let $y = \sqrt{3 x + 2} + \frac{1}{\sqrt{2 x^{2} + 4}}$

$= {(3 x + 2)}^{\frac{1}{2}} + {(2 x^{2} + 4)}^{- \frac{1}{2}}$

$∴$ $\frac{d y}{d x} = \frac{1}{2} {(3 x + 2)}^{\frac{1}{2} - 1} \cdot \frac{d}{d x} (3 x + 2) + (- \frac{1}{2}) {(2 x^{2} + 4)}^{- \frac{1}{2} - 1} \cdot \frac{d}{d x} (2 x^{2} + 4)$

$= \frac{1}{2} {(3 x + 2)}^{- \frac{1}{2}} . (3) - (\frac{1}{2}) {(2 x^{2} + 4)}^{- \frac{3}{2}} (4 x)$

$= \frac{3}{2 \sqrt{3 x + 2}} - \frac{2 x}{{(2 x^{2} + 4)}^{3 / 2}}$

Solution

Q.
If $y = \sqrt{3 x + 2} + \frac{1}{\sqrt{2 x^{2} + 4}}$ , then $\frac{d y}{d x}$ is equal to:

1 $\frac{3}{2 \sqrt{3 x + 2}} - \frac{2 x}{{(2 x^{2} + 4)}^{3 / 2}}$

2 $\frac{3}{2 \sqrt{3 x + 2}} - \frac{2 x}{{(2 x^{2} + 4)}^{3 / 2}}$

3 $\frac{3}{2 \sqrt{3 x + 2}} - \frac{2 x}{{(2 x^{2} + 4)}^{3 / 2}}$

4 None of the above

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Solution

Q. If y=3x+2+12x2+4, then dydx is equal to:

1 323x+2-2x(2x2+4)3/2

2 323x+2-2x(2x2+4)3/2

3 323x+2-2x(2x2+4)3/2