A Level Maths: Differentiation
- Jan 14, 2025
- 2 min read
Updated: Jan 21, 2025
If you've been learning or teaching the process of differentiation for the first time, then this blog post is for you! I've used my favourite graphing app - DESMOS - to make strong dynamic links between graphs & process, to reinforce the use of the differentiated function [dydx or f'(x)] to determine the gradient of the tangent to any curve plotted in the x, y plane.
Whether you're studying in the UK, Wales or worldwide, all A Level maths specifications include calculus, the mathematics of small changes. You will learn to differentiate simple functions from first principles, and to differentiate various functions by applying the relevant rules. The first expressions you'll learn to differentiate are powers of x.
I will add to this post - A level maths differentiation - over the next few weeks, answering any questions and developing materials in response to queries that are raised by students or teachers via website/Insta/LinkedIn. Please drop me a note if you have any relevant queries :)
Tangents and Normals
We are often interested in forming the equation of the tangent to a curve at a specific point. To do this we use coordinate geometry to form the equation of a straight line using the point/gradient form y-y1=m(x-x1).
The y coordinate of point (x1, y1) is obtained by substituting the x coordinate into the equation of the curve, and the gradient m of the tangent is obtained by substituting the x coordinate into the gradient function dy/dx.
If it's the normal to curve that we are interested in, then we obtain the gradient of the normal by using the relationship for perpendicular gradients, ie we calculate the negative reciprocal of the tangent gradient.
Here's a moving image to make a strong visual connection to what both lines represent.
