Question

Hi. I need help with these questions (see image) Please show workings.Answer a and b​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the chain rule along with standard derivatives

Given

y = f(g(x)) , then

$\frac{dy}{dx}$ = f'(g(x)) × g'(x)

$\frac{d}{dx}$ (sinx) = cosx , $\frac{d}{dx}$ (cosx) = - sinx

(a)

y = sin x²

$\frac{dy}{dx}$ = cos x² × $\frac{d}{dx}$ (x² )

   = cos x² × 2x

   = 2xcosx²

(b)

y = cos4x³

$\frac{dy}{dx}$ = - sin4x³ × $\frac{d}{dx}$ (4x³ )

   = - sin4x³ × 12x²

   = - 12x²sin4x³