First slide

Diffrentiation

Question

If $y = \{{(x^{2} + 2 x)}^{1 / 2}\}$ , then find $\frac{d y}{d x} .$

Moderate

A

$(x + 1) {(x^{2} + 2 x)}^{- 1 / 2}$
B

$(x + 2) {(x^{2} + 2 x)}^{- 1 / 2}$
C

$(x + 1) {(x^{2} + 1 x)}^{- 1 / 2}$
D

$(x + 1) {(x^{2} + 2 x)}^{2}$

Solution

Using the chain rule, we have
$\frac{d y}{d x} = \frac{1}{2} {(x^{2} + 2 x)}^{\frac{1}{2} - 1} (2 x + 2) = (x + 1) {(x^{2} + 2 x)}^{- 1 / 2}$

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