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

Question

asked Sep 12, 2022 114k views

1 Answer

Mephane · Answer 1 · 2022-09-19T01:21:08+0000

Answer:

(dy)/(dx) = 8(2x + 3)³

Explanation:

Differentiate using the chain rule

Given

y = f(g(x)) , then

(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

(dy)/(dx) = 4(2x + 3)³ × 2

= 8(2x + 3)³