Overview:

1. Gradient of a line passing through two points
2. Limits
3. Differentiation from first principles
4. Differentiating expressions of the form \(kx^n\) with respect to \(x\)
5. The gradient at a point on a curve
6. Tangents and normals

In part 4, we saw how to find the derivative of any function of \(x\) whose terms are of the form \(kx^n\). To find the gradient at a particular point on the curve \(y=\text{f}(x)\), we simply substitute the \(x\)-coordinate of that point into the derivative. Use this applet to see step-by=step examples and practise questions for yourself.