Question

How to differentiate this​

Answer 1

18

Explanation:

Using the product rule

Given

y = f(x). g(x) , then

`(dy)/(dx)` = f(x). g'(x) + g(x). f'(x)

Here

f(x) =
`(2x+3)^(5)` ⇒ f'(x) = 5
`(2x+3)^(4)` ×
`(d)/(dx)` (2x + 3) , then

f'(x) = 10
`(2x+3)^(4)`

g(x) =
`(x+2)^(8)` ⇒ g'(x) = 8
`(x+2)^(7)` ×
`(d)/(dx)` (x + 2) , then

g'(x) = 8
`(x+2)^(7)`

Thus

`(dy)/(dx)` =
`(2x+3)^(5)` . 8
`(x+2)^(7)` +
`(x+2)^(8)` . 10
`(2x+3)^(4)` ← factor expression

=
`(2x+3)^(4)`
`(x+2)^(7)` [ 8(2x + 3) + 10(x + 2)

=
`(2x+3)^(4)`
`(x+2)^(7)` (16x + 24 + 10x + 20)

=
`(2x+3)^(4)`
`(x+2)^(7)` (26x + 44)

Thus

`(dy)/(dx)` ( x = - 1)

=
`1^(4)` ×
`1^(7)` × 18

= 1 × 1 × 18

= 18

Answer 2

Explanation:

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