Question

Hi. I need help with this question (see image). Please show workings.
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Answer 1

`(dy)/(dx)` = -
`(18x)/((3x^2+1)^4)`

Explanation:

Differentiate using the chain rule

Given

y = f(g(x)) , then

`(dy)/(dx)` = f'(g(x) × g'(x)

Given

y =
`(1)/((3x^2+1)^3)` =
`(3x^2+1)^(-3)` , then

`(dy)/(dx)` = - 3
`(3x^2+1)^(-4)` ×
`(d)/(dx)` (3x² + 1 )

= - 3
`(3x^2+1)^(-4)` × 6x

= -
`(18x)/((3x^2+1)^(4) )`