Question

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

Answer 1

Derivative of `f(x)` comes to be `(6x(2x-1)-2(3x^2-4))/(2x-1)^2`.

Explanation:

Let, `y=f(x)=(3x^2-4)/(2x-1).`
Therefore, Differentiating `y` w.r.t `x` comes to be,

`dy/dx=(v*(du)/dx-u*(dv)/dx)/v^2`
`:.dy/dx=((2x-1)*d/(dx)(3x^2-4)-(3x^2-4)*d/(dx)(2x-1))/(2x-1)^2`

`:.dy/dx=((2x-1)*(3*2*x^(2-1)-0)-(3x^2-4)*(2-0)`
`:.dy/dx=(6x(2x-1)-2(3x^2-4))/(2x-1)^2`. (answer).