Calculus Section 2.2 Basic Differentiation Rules and Rates of Change

The Constant Rule For every x value, the slope is always 0. Therefore, the derivative of a constant function is 0. What is the slope of the graph of the function f(x) = 6?

The Power Rule

The Constant Multiple Rule

The Sum and Difference Rules

Derivatives of Polynomials

A Constant Times a Variable to an Exponent Rewrite the function to get the terms as a constant times a variable to an exponent. A CONSTANT TIMES A VARIABLE TO AN EXPONENT!!!!

Radicals to Rational Exponents

Derivatives of Sine and Cosine Functions

Rates of Change The derivative is the rate of change of one variable with respect to another. Usually we talk about the rate of change of y with respect to x.

Vertical Motion of an Object The function s(t) that gives the position of an object (relative to the origin) as a function of time t is called the position function.

Position Function Where g is the acceleration due to gravity, v 0 is the initial velocity, and s 0 is the initial position of the object.

Average Velocity

Instantaneous Velocity The velocity function is the derivative of the position function (i.e. the rate of change of the position function at any instant of time t).

Acceleration The acceleration function is the derivative of the velocity function (i.e. the rate of change of the velocity function at any time t).