Product rule, quotient rule and the remaining trigonometric derivatives

Learning objectives

Apply the product rule to differentiate a product of two or more functions, and simplify the result where required

Apply the quotient rule to differentiate a quotient of two functions, and decide when rewriting a quotient as a product with a negative power is simpler

Derive the derivatives of tan x, cot x, sec x and csc x from the quotient rule, and recall and use them fluently

Combine the product, quotient and basic rules to differentiate expressions, and use them with tables or graphs of f, g, f′ and g′ to evaluate derivatives of products and quotients at a point

Use the product and quotient rules in context, for example to find the rate of change of a quantity that is a product or a ratio of two changing quantities