Differentiation: standard functions, chain, product and quotient rules
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 3 worked examples, 6 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- How fast is it changing?
- The standard derivatives
- The chain rule
Read the transcript of the teaching part
Last time
Before we start: last time, in Linked progressions, progressions in context, trigonometric terms, and sums in a range, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
How fast is it changing?
The speedometer of a car shows how quickly the distance is changing, right now. That instant rate of change is the derivative. To differentiate quickly you need a short list of standard results, and three rules for combining them.
The standard derivatives
The derivative of x to the n is n x to the n minus one. e to the x differentiates to itself. ln x differentiates to one over x. Sine goes to cosine, and cosine goes to minus sine. Tangent goes to secant squared. Cambridge expects these in radians.
The chain rule
If y is a function of u, and u is a function of x, then dy by dx equals dy by du, times du by dx. In practice: differentiate the outer function, leave the inside alone, then multiply by the derivative of the inside. The derivative of sine of five x plus three is five cosine of five x plus three.
Chapter 1.7: Differentiation
- Differentiation: standard functions, chain, product and quotient rules 5 min
- Tangents and normals 5 min
- Stationary points and the derivative tests 6 min
- Connected rates of change and small increments 6 min
- Maximum and minimum problems, and stationary points with integration 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.