Differentiate the following functions with respect to x:

Question

Philoid · Accepted Answer

Let, y =

We have to find dy/dx

As we can observe that y is a fraction of two functions say u and v where,

u = ax² + bx + c and v = px² + qx + r

∴ y = u/v

As we know that to find the derivative of fraction of two function we apply quotient rule of differentiation.

By quotient rule, we have –

…equation 1

As, u = ax² + bx + c

∴ …equation 2 {∵ }

As, v = px² + qx + r

∵ , so we get –

…equation 3

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2 and 3}

⇒

Hence,