Question

differenciate the following function with respect to x; a) (3x^2 +2)^2​

Answer 1

Given :

(3x² + 2)²

To find :

Differentiation of given function with respect to x

$\sf \: \dfrac{d}{dx}{(3x^2\:+2\:)}^{2}$

Identity used :

$\sf \bullet \: \: \: \dfrac{d}{dx} {x}^{n } = n \: \times {x}^{(n - 1)} \\ \\ \sf \bullet \: \: \: \dfrac{d}{dx} C \: = 0 \: \: (here \: C \: is \: constant)$

Solution :

$\sf \implies \dfrac{d}{dx}{(3x^2\:+2\:)}^{2} \\ \\ \sf \implies \: 2 \times {(3 {x}^{2} + 2)}^{(2 - 1)} \times \dfrac{d}{dx} (3 {x}^{2} + 2) \\ \\ \sf \implies \: 2 \times (3 {x}^{2} + 2) \times ( \dfrac{d}{dx} 3 {x}^{2} + \dfrac{d}{dx} 2) \\ \\ \: \sf \implies \: 2 \times (3 {x}^{2} + 2) \times( \: (3 \times 2 {x}^{(2 - 1)}) + 0) \\ \\ \sf \implies \: 2 \times (3 {x}^{2} + 2) \times(6x + 0) \\ \\ \sf \implies \: 12 x\times (3 {x}^{2} + 2) \\ \\ \sf \implies \: 12 {x}^{3} + 24x$

ANSWER :

12x³ + 24x