Differentiate the following function with respect of `x \ :(a x^2+b x+c)/(p x^2+q x+r)`

Explanation

Let us consider `y =(a x^2+b x+c)/(p x^2+q x+r)`

We need to find dy/dx

We know that y is a fraction of two functions say u and v where, u = `ax^2 + bx + c` and `v = px^2 + qx + r`

∴ y = u/v

Now let us apply quotient rule of differentiation. By using quotient rule, we get

(du/dx)=2ax+b

(dv/dx)=2px+q

Thus` (dy/dx)=(v.(du/dx)-u(dv/dx))/v^2`

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