Functions, Limits & Derivatives
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Key formulas
Power Rule
Multiply by exponent, reduce exponent by 1.
Log Derivative
Derivative of inner function divided by inner function.
Part 1 of 2
1. Domain Restrictions & Inequality Systems
Finding the domain of composite functions requires solving a system of simultaneous inequalities:
- Denominators: set ≠ 0.
- Even Roots: set radicand ≥ 0.
- Logarithms: set argument > 0.
Worked example
f(x) = ln(x − 2) / √(9 − x²). Log argument: x − 2 > 0 → x > 2. Square root denominator: 9 − x² > 0 → −3 < x < 3. Intersection: x ∈ (2, 3).
1.The argument of a natural logarithm can be negative as long as the base is e.
2.If a denominator contains ln(x), x = 1 must be excluded from the domain.
Exam strategy
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