Question

How do you differentiate `-1/(r-2)^2`?

Answer 1

`d/(dr)(-1/(r-2)^2)=2/(r-2)^3`

Explanation:

In order to use the chain rule, let `u=r-2`. Then `(du)/(dr)=1`. We are now differentiating

`-1/(r-2)^2=-1/u^2=-u^-2`

with respect to r. Using the power rule, the derivative is

`d/(dr)(-u^-2)=2u^-3*(du)/(dr)=2u^-3=2(r-2)^-3=2/(r-2)^3`