Pages similar to: Derivatives of more general power functions A refresher on the chain rule How to compute the derivative of a composition of functions. Derivatives of polynomials How to compute the derivative of a polynomial. 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. 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. 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. The second and higher derivatives Taking derivatives multiple times to calculate the second or higer derivative. Implicit differentiation Differenting a function that is defined implicitly in terms of a relation between two variables. Inflection points, concavity upward and downward Finding points where the second derivative changes sign. Achieving desired tolerance of a Taylor polynomial on desired interval For a given interval around a point, how many terms of a Taylor polynomial expanded around that point must be used to achieve a required tolerance? Newton's Method A method to approximate the roots to an equation. Tangent and normal lines How to compute the tangent and normal lines to the graph of a function. Taylor polynomials: formulas Different ways of writing Taylor's formula with remainder term. 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. The idea of the derivative of a function The derivative of a function as the slope of the tangent line. Determining tolerance/error in Taylor polynomials. Calculating with what tolerance a Taylor polynomial approximates a function on an interval. How large an interval with given tolerance for a Taylor polynomial? Given a Taylor polynomial expanded around a point, on how large an interval around the point does it achieve a required tolerance? Computational tricks regarding Taylor polynomials A short cut to calculating Taylor polynomials in terms of Taylor polynomials of simple functions.