Pages similar to: Tangent and normal lines
- The idea of the derivative of a function
The derivative of a function as the slope of the tangent line. - Developing intuition about the derivative
An intuitive exploration into the properties of the derivative, illustrated by interactive graphics. - Calculating the derivative of a linear function using the derivative formula
Exploring how the limit definition of the derivative gives the slope of a linear function. - Introduction to differentiability in higher dimensions
An introduction to the basic concept of the differentiability of a function of multiple variables. Discussion centers around the existence of a tangent plane to a function of two variables. - The multivariable linear approximation
Introduction to the linear approximation in multivariable calculus and why it might be useful. - Derivatives of polynomials
How to compute the derivative of a polynomial. - Derivatives of more general power functions
How to compute the derivative of power functions. - A refresher on the quotient rule
How to compute the derivative of a quotient. - A refresher on the product rule
How to compute the derivative of a product. - A refresher on the chain rule
How to compute the derivative of a composition of functions. - Linear approximations: approximation by differentials
Approximating the value of a function near a point by its tangent line formula. - Implicit differentiation
Differenting a function that is defined implicitly in terms of a relation between two variables. - Related rates
Calculating one derivative in terms of another derivative. - Intermediate Value Theorem, location of roots
Using the Intermediate Value Theorem to find small intervals where a function must have a root. - Derivatives of transcendental functions
A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. - L'Hospital's rule
A way to simplify evaluation of limits when the limit is an indeterminate form. - The second and higher derivatives
Taking derivatives multiple times to calculate the second or higer derivative. - Inflection points, concavity upward and downward
Finding points where the second derivative changes sign. - The idea of the chain rule
An illustration of the basic concept of the chain rule using interactive graphics to diagram the relevant points on the graphs and the corresponding slopes. - Simple examples of using the chain rule
Basic examples that show how to use the chain rule to calculate the derivative of the composition of functions.
Back to: Tangent and normal lines