Question

How do you use the chain rule to differentiate `y=7/(x^2+x)^2`?

Answer 1

This can be written as `y = 7(x^2 + x)^-2`.

We let `y = 7u^-2` and `u = x^2 +x`. Then `dy/(du) = -2u^-1 = -14/u` and `(du)/dx = 2x + 1`

`dy/dx = dy/(du) * (du)/dx`

`dy/dx = -14/u * 2x + 1`

`dy/dx = (-14(2x + 1))/(x^2 + x)`

Hopefully this helps!