Question

Use the chain rule to find the derivative of each of the following :

a.
`(2)/((3x^2-x+7)^3)`

b.
`(4x-10)^1^0`

Answer 1

see explanation

Explanation:

Using the chain rule

Given

y = f(g(x)), then

`(dy)/(dx)` = f'(g(x)) × g'(x)

(a)

y =
`(2)/((3x^2-x+7)^3)` = 2 (
`3x^2-x+7)^(-3)`

`(dy)/(dx)` = 2. - 3
`(3x^2-x+7)^(-4)` ×
`(d)/(dx)` (3x² - x + 7)

= - 6
`(3x^2-x+7)^(-4)` × (6x - 1)

=
`(-6(6x-1))/((3x^2-x+7)^4)`

---------------------------------------------------

(b)

y =
`(4x-10)^(10)`

`(dy)/(dx)` = 10
`(4x-10)^(9)` ×
`(d)/(dx)`(4x - 10)

= 10
`(4x-10)^(9)` × 4

= 40
`(4x-10)^(9)`