First slide

Diffrentiation

Question

If $y = {[x^{2} + 3 x + 2]}^{3} + [\log_{e} x^{2}] .$ Then, find $\frac{d y}{d x} .$

Moderate

A

$(2 x + 3) {(x^{2} + 3 x + 2)}^{2} + \frac{2}{x}$
B

$3 (2 x + 3) {(x^{2} + 3 x + 2)}^{2} + \frac{2}{x}$
C

$3 (2 x + 3) {(x^{2} + 3 x + 2)}^{3} + \frac{2}{x}$
D

$3 (2 x + 3) {(x^{2} + 3 x + 2)}^{2}$

Solution

Using the chain rule, we have
$\frac{d y}{d x} = 3 {(x^{2} + 3 x + 2)}^{3 - 1} \cdot (2 x + 3) + \frac{1}{x^{2}} \cdot 2 x = 3 (2 x + 3) {(x^{2} + 3 x + 2)}^{2} + \frac{2}{x}$

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