Question

How do you differentiate `f(x) = (3 + 4x)/(1 + x^2)`?

Answer 1

The quotient rule, which we'll use here, states that, be `y=f(x)/g(x)`, then `y'=(f'(x)g(x)-f(x)g'(x))/(g(x)^2)`.

Thus,

`y'=(4*(1+x^2)-(3+4x)*2x)/(1+x^2)^2`

`y'=(4+4x^2-6x-8x^2)/(1+x^2)^2`

`y'=(-4x^2-6x+4)/(1+x^2)^2`