Question

How do you differentiate `f(x) =(1-5x)/(2x^2+7)` using the quotient rule?

Answer 1

`f'(x)=(10x^2-4x-35)/((2x^2+7)^2`

Explanation:

The quotient rule states that :

`d/dx[f(x)/g(x)]=(g(x)*f'(x)-f(x)*g'(x))/([g(x)]^2)`.

Application to this particular function yields :

`f'(x)=((2x^2+7)(-5)-(1-5x)(4x))/(2x^2+7)^2`

`=(10x^2-4x-35)/((2x^2+7)^2`.