Question

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

Answer 1

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

Explanation:

Let `g(x)=u`

Then `(d(1/u))/dx=(d(u^-1))/dx`

Applying power rule,

`" "d((u^-1))/dx=(-u^-2)(du)/dx" "...(1)`

Here `u=(x+2)` and `(du)/dx=1`

Plugging these in `(1)`, we get `(d(1/(x+2)))/dx=-1/(x+2)^2`