Learning objectives
Recognize a composite function and identify its outer and inner functions, including compositions of three or more functions
Apply the chain rule in the form d/dx[f(g(x))] = f′(g(x)) · g′(x), and in Leibniz form dy/dx = dy/du · du/dx, to differentiate powers, exponentials, logarithms and trigonometric functions of other functions
Combine the chain rule with the product and quotient rules to differentiate more complicated expressions, and simplify the answer
Evaluate derivatives of composite functions at a point using tables or graphs of f, g, f′ and g′
Differentiate general exponential and logarithmic functions such as aˣ and logₐ x, and expressions such as e^(kx) and ln(g(x)), using the chain rule
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