Question

How do you find the derivative of `1/(1+x^2)`?

Answer 1

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

Explanation:

We use Chain Rule here. In order to differentiate a function of a function, say `y=f(g(x))`, where we have to find `(dy)/(dx)`, we need to do (a) substitute `u=g(x)`, which gives us `y=f(u)`. Then we need to use a formula called Chain Rule, which states that `(dy)/(dx)=(dy)/(du)xx(du)/(dx)`.

Here we have `y=1/g(x)` where `g(x)=1+x^2`

Hence `(dy)/(dx)=(df)/(dg)xx(dg)/(dx)`

= `-1/(1+x^2)^2xx2x=-(2x)/(1+x^2)^2`