Question

How do you differentiate `f(x)=4/(x+1)^2` using the chain rule?

Answer 1

`f'(x)=-8/(x+1)^3`

Explanation:

Express `f(x)=4(x+1)^-2`

differentiate using the `color(blue)"chain rule"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))`

let `u=x+1rArr(du)/(dx)=1`

and `y=4u^-2rArr(dy)/(du)=-8u^-3`

substitute these values into `dy/dx` writing u in terms of x.

`dy/dx=-8u^-3 xx1=-8/(x+1)^3`