Question

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

Answer 1

The quotient rule states that for `f(x)=g(x)/h(x)`, then `(df(x))/(dx)=(g'(x)h(x)-g(x)h'(x))/h(x)^2`

Explanation:

Derivating it following the quotient rule, then:

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

`(df(x))/(dx)=(-2x^2+2+2x+4x^2)/(1-x^2)^2`

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