Differentiation rules and standard derivatives

Learning objectives

Differentiate xⁿ for rational n, sin x, cos x, eˣ and ln x, and sums and constant multiples of these functions

Apply the chain rule to differentiate composite functions, including powers, exponentials, logarithms and trigonometric functions of a function

Apply the product rule and the quotient rule, and combine them with the chain rule to differentiate more complex expressions

(HL) Differentiate tan x, sec x, cosec x, cot x, aˣ, logₐ x, arcsin x, arccos x and arctan x, and composites of these with a linear function

(HL) Differentiate relations defined implicitly, such as x² + xy + y² = 7, and find the gradient of an implicitly defined curve at a point