Question

How do you differentiate `f(x)= (4 x^2 + 5x -3 )/ (x- 1 )` using the quotient rule?

Answer 1

`f' (x)=(4x^2 -8x - 2)/(x-1)^2`

Explanation:

From the given `f(x) = (4x^2+5x-3)/(x-1)`

Use `d/dx(u/v)= (v (du)/dx - u (dv)/dx)/(v^2)`

let `u=4x^2+5x-3`

let `v=x-1`

Answer 2

I found `f'(x)=(4x^2-8x-2)/(x-1)^2`

Explanation:

Consider the Quotient Rule:

We can apply this to your function to get:
`f'(x)=((8x+5)(x-1)-1*(4x^2+5x-3))/(x-1)^2=`
`=(8x^2-8xcancel(+5x)-5-4x^2cancel(-5x)+3)/(x-1)^2=`
`=(4x^2-8x-2)/(x-1)^2`