How do I differentiate a quadratic to the power n?

To do this we will use the chain rule, whereby dy/dx = dy/du * du/dx. So if y = (ax^2+bx+c)^n then we will say that u = ax^2+bx+c. Therefore y =u^n. So to find dy/dx we differentiate u with respect to x, which = 2ax +b, and multiply this by the differential of y =u^n, which is nu^(n-1). Therefore dy/dx = nu^(n-1) * (2ax+b) Subbing the original equation in for u leads to dy/dx = n(2ax+b)(ax^2+bx+c)^(n-1)

AA
Answered by Alex A. Maths tutor

5580 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Identify the stationary points of f(x)=3x^3+2x^2+4 (by finding the first and second derivative) and determine their nature.


y = (x^3)/3 - 4x^2 + 12x find the stationary points of the curve and determine their nature.


The radius of a circular disc is increasing at a constant rate of 0.003cm/s. Find the rate at which the area is increasing when the radius is 20cm.


Find dy/dx when y = x^2(cos(x)).


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning