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

see explanation

Step-by-step explanation:

Using the chain rule along with standard derivatives

Given

y = f(g(x)) , then

= f'(g(x)) × g'(x)

(sinx) = cosx , (cosx) = - sinx

(a)

y = sin x²

= cos x² × (x² )

   = cos x² × 2x

   = 2xcosx²

(b)

y = cos4x³

= - sin4x³ × (4x³ )

   = - sin4x³ × 12x²

   = - 12x²sin4x³

answer: options

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .