From gradient to derivative
From gradient to derivative
A straight line has one constant gradient, but a curve can have a different gradient at each point. To get the gradient at one point on a curve, we draw the tangent there.
Step-by-step lessons on Edexcel A Level Maths Differentiation, covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation. Each one builds up to exam-style questions. Build fluency with the core pure algebra and calculus toolkit early, since almost every mechanics and statistics topic on the course depends on it.