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Topic 5: Further differentiation

Differentiation rules

11 hours

• Use the chain rule, if 𝑦 = 𝑓(𝑢) and 𝑢 = 𝑔(𝑥) then 𝑑𝑦 𝑑𝑥 = 𝑑𝑦 𝑑𝑢 × 𝑑𝑢 𝑑𝑥, to determine the derivative of composite functions involving power and polynomial functions. 1 interactive
• Use the product rule, 𝑑(𝑢𝑣) 𝑑𝑥 = 𝑢 𝑑𝑣 𝑑𝑥 + 𝑣 𝑑𝑢 𝑑𝑥, to determine the derivative of products of functions involving power and polynomial functions.
• Use the quotient rule, 𝑑(𝑢 𝑣) 𝑑𝑥 = 𝑣𝑑𝑢 𝑑𝑥−𝑢𝑑𝑣 𝑑𝑥 𝑣2, to determine the derivative of quotients of functions involving power and polynomial functions.
• Solve problems that involve combinations of the chain rule, product rule and quotient rule to differentiate functions involving power and polynomial functions, expressing derivatives in simplest and factorised form.