Differentiation

Differentiating any function you can write down: exponentials, logarithms and trigonometric functions, combined in every way. DfE content area G · standard derivatives, the chain, product and quotient rules, implicit and parametric curves, concavity and connected rates of change.

• An Overview — the standard derivatives, the three combining rules, the language and the common mistakes

The content statements

• Exponentials, Logs and Trig — derivatives of e^kx, a^kx, ln x, sin kx, cos kx and tan kx, with first-principles proofs for sin and cos
• Chain, Product and Quotient Rules — composite functions, products and quotients, and dy/dx = 1 ÷ (dx/dy)
• Implicit and Parametric Differentiation — gradients, tangents, normals and stationary points of implicit and parametric curves
• Concavity and Points of Inflection — the second derivative, convex and concave curves, and where they change
• Connected Rates of Change — related rates by the chain rule, and setting up simple differential equations

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.