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Derivative formula given for functions of the form f(x) = xn, derived using the binomial theorem.
Proof by induction of derivative formula for xn.
Derivative formula for un, proven by induction.
Derivative formula found for functions of the form f(x) = xa, where a is a fraction.
Algebraic rules for exponentials and logarithms are reviewed.
Derivation, leading to the definition of e and the natural logarithm.
Derivation using the chain rule. Derivative of ln(x) also given and used to find the numeric value of e.
Finding the derivative of a product of functions using logarithms to convert into a sum of functions. Includes worked example.
Angles and continuous functions of them are described abstractly, with mention of the specific functions sin, cos, tan, sec, csc, and cot.
Angle addition formulas and other trigonometric identities involving sin and cos.
Derivation using trig identities and difference quotients.
Derivative of tan(x) is derived from the quotient rule and the derivatives of sin(x) and cos(x). Derivatives for sec(x), csc(x), and cot(x) are also stated.
Brief definitions of the inverse trigonometric functions sin-1(x), cos-1(x), and tan-1(x)
Formulas for the derivatives of the inverse trigonometric functions, as well as the equation sin-1(x) + cos-1(x) = pi/2.
Definition, including the properties of the function and its derivatives, as well as a graph of the function.
List of important properties, as well as the derivatives of sine and cosine and a power series representation of sine and cosine.
Deriving further rules for derivatives, including the product rule and the rule for functions of the form xn.
Derivatives for the identity, exponential, and sine functions.
Finding the equation for the tangent line to an exponential function through a point not on the graph of the function.
Taking the first and second derivatives of a function involving an exponential and a cosine.
Finding the derivatives of an exponential function.
Finding the derivatives of exponential and logarithmic functions.
Finding the derivatives of two trigonometric functions.
Evaluating the derivative of the inverse of an exponential function.
Four-part question involving the evaluation of three derivatives and a limit.
Sketching the graph of the inverse sine function and finding its derivative.
Two questions finding the derivatives of functions.
Finding the derivatives of four functions.
A list of trigonometric and inverse trigonometric identities and formulas involving integrals and derivatives.
Three derivatives to be evaluated using a variety of techniques.
Five questions which involve taking derivatives and antiderivatives of polynomials, finding the points on a graph which have horizontal tangent lines, and finding derivatives of rational functions.
Five questions which involve finding second, third, or nth derivatives of functions.
Five questions which involve evaluating derivatives and limits of functions which contain logarithms or exponentials, graphing an exponential function, and calculating interest compounded with different frequencies.
Four questions which involve calculating derivatives of trigonometric functions.
Three questions which involve evaluating five differentials and twenty indefinite integrals using a range of techniques.
Six questions which involve evaluating integrals and derivatives of these functions, as well as graphing them and finding tangent lines or average values.