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

5576 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the equation of the tangent to the curve y = 3x^2 + 4 at x = 2 in the form y = mx + c


C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.


Solve x^2 > |5x - 6|


How to transform graphs of functions?


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