22 resources.
The chain rule for differentiating composite functions, with two worked derivative examples.
What a definite integral is and how to evaluate one, with a worked trigonometric example.
The power rule for differentiating x to a fixed exponent, with a worked example on a square root.
The product rule for differentiating a product of two functions, with worked examples including logarithmic differentiation.
The quotient rule for differentiating one function divided by another, with worked examples.
Using derivatives as rates of change, with worked examples on a growing circle's area and a particle's velocity and acceleration.
How to differentiate an equation that isn't already solved for y, with worked examples including an inverse trig identity.
How the sign of a function's derivative determines where it's increasing or decreasing, with worked examples including a cubic.
Finding local maxima and minima and solving optimization problems using derivatives, with worked examples.
What Rolle's theorem states and how to verify it for a function on a closed interval, with a worked example.
How the derivative gives the tangent's slope and the normal's slope is its negative reciprocal, with a worked example.
Finding the slope of a tangent line to a curve at a given point, with worked examples on a cubic and a rational function.
Splitting a rational function into simpler fractions before integrating, with worked examples.
Standard integration formulas for functions like 1/(x^2-a^2) and 1/(a^2-x^2), with worked examples.
Rewriting a trigonometric integrand with an identity before integrating, with worked examples on cos^2 x, sin^2 x, and a secant identity.
A shortcut formula for integrating e^x times a function plus its own derivative, with a worked example.
Using definite integrals to find area under a curve, including a full period of cosine and a classic circle-area derivation.
How to form a differential equation from a family of curves, and how to solve one by separating variables, with worked examples.
The integration by parts formula for integrating a product of two functions, with a worked example.
Left-hand and right-hand derivatives, spotting a point that's continuous but not differentiable, and finding a function's domain, with worked examples.
Using differentials to approximate square roots and estimate small changes, with worked examples including a percentage-change setup.
How to take partial derivatives of a multivariable function, with a worked example that also verifies equality of mixed second partial derivatives by direct computation.