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Differentiation (Metric)

Class Details

Tom Baker

Learn, or revise, differentiation from first principles, techniques of differentiation and using differentiation to sketch curves and solve problems.

Principles

The gradient of a curve as the limit of the gradient of a secant or chord. This is an A-level topic, but sometimes a bit neglected at that level.

Gradient of a curve at a point as the limit of the gradient of a secant or chord; the idea of the derivative.

Lesson

Techniques

Differentiating key functions, and sums, products, quotients and composites. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.

Differentiating functions of the form \(a\,f(x)+b\,g(x)\).

Lesson

Differentiating functions of the form \(f(x)\,g(x)\).

Lesson

Differentiating functions of the form \(f(x)/g(x)\).

Lesson

Differentiating functions of the form \(f(g(x))\).

Lesson

Putting the rules of differentiation to use.

Lesson

Differentiating functions given implicitly, in equations of the form \(f(x,\,y)=0\).

Lesson

The \(n\)th derivative of a product.

Lesson Not yet graded

Key results to do with differentiation.

Lesson Not yet graded

Applications

Using differentiation to find stationary points and points of inflexion on curves, and to solve problems involving velocity and acceleration. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.

The result \(f(x)=f(0)+x\,f'(0)+x^2/2!\,f''(0)+\dots\).

Lesson Not yet graded

Points where a curve is locally horizontal; how to find and classify them.

Lesson

Finding points where a curve changes its direction of curvature.

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