Calculus I Ms. Plata 2010

Fortunately, several rules have been developed for finding derivatives without having to use the definition directly. Why? These formulas greatly simplify the task of differentiation

 In Leibniz notation, we write this rule as follows:  Example:

 If n is a positive integer, then:  Example:

 If c is a constant and f is a differentiable function, then:  Example:

 If f and g are both differentiable, then: The derivative of a sum of functions is the sum of the derivatives.  The difference Rule:

The derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative first function

 If f and g are both differentiable, then:  Example:

The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

 If f and g are differentiable, then