Question

Find the derivative with respect to x of y = (3x + x^2)^5

Answer 1

The required "option A) $5(3x + x^2)^{4} (3+2x)$" is correct.

Step-by-step explanation:

We have,

$y = (3x + x^2)^5$          ..... (1)

To find, $\dfrac{dy}{dx}$ = ?

Differentiating equation (1) w.r.t. 'x', we get

$\dfrac{dy}{dx}= \dfrac{d[(3x + x^2)^5]}{dx}$

⇒ $\dfrac{dy}{dx}=5(3x + x^2)^{5-1} \dfrac{d(3x + x^2)}{dx}$

[ ∵ $y=x^{n}$ ⇒ $\dfrac{dy}{dx}=nx^{n-1}$]

⇒ $\dfrac{dy}{dx}=5(3x + x^2)^{4} (3(1) + 2x^{2-1})$

⇒ $\dfrac{dy}{dx}=5(3x + x^2)^{4} (3+2x)$

Thus, the required "option A) $5(3x + x^2)^{4} (3+2x)$" is correct.