Question

How do you use the chain rule to differentiate `y=(x^2+4)^-1`?

Answer 1

`u = x^2 +4`, therefore `y = u^-1`

`(du)/dx = 2x`

`(dy)/(du) = (-u^-2)`

`(dy)/(dx) = ((du)/(dx))((dy)/(du)) = (2x)(-u^-2) = (2x)((x^2 +4)^-2) = (2x)/(x^2 +4)^2`