Question

How to differentiate

Answer 1

First of all, substitute
`u^2` in the first expression:

`u = (b)/(x+1) \implies u^2 = (b^2)/((x+1)^2)`

So, your function is

`y = (a)/((b^2)/((x+1)^2)) = (a(x+1)^2)/(b^2) = (a)/(b^2)(x+1)^2`

Since a and b are constants, we have

`(dy)/(dx) (a)/(b^2)(x+1)^2 = (a)/(b^2)(dy)/(dx)(x+1)^2`

The derivative of
`(x+1)^2` is

`2(x+1)\cdot 1`

following the rule

`(d)/(dx) f^n(x) = nf^(n-1)(x)f'(x)`

So, the answer is

`(dy)/(dx) (a)/(b^2)(x+1)^2 = (2a)/(b^2)(x+1)`

Answer 2

`(dy)/(dx)` = 2a/b²(x + 1)

y = a/u² = a/ (b²/(x + 1)²) = a/b² (x + 1)²

differentiate using the ' chain rule'

`(dy)/(dx)` = 2a/b² (x + 1)