Question

Hi. I need help with this question (see image). Please show workings.​

Answer 1

Answer:

$\frac{dy}{dx}$ = 8(2x + 3)³

Step-by-step explanation:

Differentiate using the chain rule

Given

y = f(g(x)) , then

$\frac{dy}{dx}$ = f'(g(x)) × g'(x)

Here

f(x) = $(2x+3)^{4}$ ⇒ f'(x) = 4(2x + 3)³

g(x) = 2x + 3 ⇒ g'(x) = 2

Thus

$\frac{dy}{dx}$ = 4(2x + 3)³ × 2

    = 8(2x + 3)³