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1.10.4 Product, quotient and chain rules (A-level only)

Which rule is required by the main structure of x2sin⁡xx^2\sin xx2sinx?

A

If y=f(x)y=f(x)y=f(x) and an inverse exists, then dxdy=1dydx\displaystyle \frac{dx}{dy}=\frac{1}{\frac{dy}{dx}}dydx​=dxdy​1​. This reciprocal relationship requires dydx≠0\boxed{\displaystyle \frac{dy}{dx}\neq0}dxdy​=0​.

B

In the quotient rule, the numerator is vu′−uv′\boxed{vu'-uv'}vu′−uv′​, and the rule requires v≠0v\neq0v=0.

C

The product rule.

D

For composite functions, ddxsin⁡(g(x))=\frac{d}{dx}\sin(g(x))=dxd​sin(g(x))= cos⁡(g(x))g′(x)\boxed{\cos(g(x))g'(x)}cos(g(x))g′(x)​ and ddxeg(x)=\frac{d}{dx}e^{g(x)}=dxd​eg(x)= eg(x)g′(x)e^{g(x)}g'(x)eg(x)g′(x).

1.10.4 Product, quotient and chain rules (A-level only) Flashcards

  1. A Level
  2. /Maths
  3. /1.10.4 Product, quotient and chain rules (A-level only)

Flashcards for AQA A Level Maths 1.10.4 Product, quotient and chain rules (A-level only), covering the key formulae, methods and definitions you need to recall for Paper 1, Paper 2 and Paper 3. 22 cards, matched to the AQA A Level Maths (7357) specification. Recall questions account for roughly 50% of marks at A Level Maths, so these target the marks you can secure before the paper starts.