Differentiation

Hold infinity in the palm of your hand.

This picture illustrates one of the more frightening rides at an amusement park.
To ensure that the ride is absolutely safe, its designers need to know the gradient of the curve at any point. What do we mean by the gradient of a curve?

The gradient of a curve.

Differentiating by using standard results

The method of differentiation from first principles will always give the gradient function, but it is rather tedious and, in practice, it is hardly ever used. Its value is in establishing a formal basis for differentiation rather than as a working tool.

Using differentiation.

Tangents and Normals