Differentiate the following w.r.t. $x$ .
$(x + 5)^{- 1 / 2}$ .

- \frac{1}{2} (x + 5)^{- 1 / 2}

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- \frac{1}{2} (x + 5)^{- 3 / 2}

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- \frac{1}{3} (x + 5)^{- 3 / 2}

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- \frac{1}{2} (x + 5)^{- 5 / 2}

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Solution

The correct option is A $- \frac{1}{2} (x + 5)^{- 3 / 2}$
$\frac{d}{d x} {(x + 5)}^{- 1 / 2}$
$= - \frac{1}{2} {(x + 5)}^{- 1 / 2 - 1} . \frac{d}{d x} (x + 5)$
$= - \frac{1}{2} {(x + 5)}^{- 3 / 2} {1 + 0}$
$= - \frac{1}{2} {(x + 5)}^{- 3 / 2}$

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Solve the equations:

(i) 5x = 3x + 24;

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(iii) 7x − 10 = 4x + 11;

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(vii) ;

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(xiv) .

\int \sqrt{(x^{2} + 2 x + 5)} d x

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