Question

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

Answer 1

see explanation

Explanation:

Using the chain rule along with standard derivatives

Given

y = f(g(x)) , then

`(dy)/(dx)` = f'(g(x)) × g'(x)

`(d)/(dx)` (sinx) = cosx ,
`(d)/(dx)` (cosx) = - sinx

(a)

y = sin x²

`(dy)/(dx)` = cos x² ×
`(d)/(dx)` (x² )

= cos x² × 2x

= 2xcosx²

(b)

y = cos4x³

`(dy)/(dx)` = - sin4x³ ×
`(d)/(dx)` (4x³ )

= - sin4x³ × 12x²

= - 12x²sin4x³