3.3 Techniques of DifferentiationDerivative of a Constant

(page 191)

The derivative of a constant function is 0.

Derivative of x to a Power(page 191)

To differentiate x to any integer power,multiply that power by x raised to the next lowest integer power.

Derivative of x to a PowerExample 7

(page 196)

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Derivative of a Constant Times a Function

(page 192)

A constant factor can be moved through a derivative sign.

Derivatives of Sums and Differences

(page 192-193)

The derivative of a sum equals the sum of the derivatives,and the derivative of a difference equals the difference of the derivative.

Derivatives of Sums and Differences - Examples

(page 193)

Derivative of a Product(page 193)

The derivative of a product of two functions is the firstfunction times the derivative of the second plus thesecond times the derivative of the first.

Derivative of a Product Examples

(page 194)

Derivative of a product of polynomials can be done by twomethods. One method is to follow the derivative of a product rule. The other method is to expand the product andthen use previously presented derivative rules.

Derivative of a Product Examples

(page 194)

Derivative of a Product Examples

(page 194)

Derivative of a Quotient(page 193-194)

The derivative of a quotient of two functions is the denominatortimes the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the denominator squared.

Derivative of a QuotientExample 6a,b

(page 195)

Derivative of a QuotientExample 6b

(page 195)

6b For the function in example 6, find the exact location of thehorizontal tangent lines.

Derivative of a QuotientExample 6b

(page 196)

Derivative of a Reciprocal(not in new edition)

The derivative of the reciprocal of a function is the negativeof the derivative of the function divided by the function squared.

This relationship is actually an application of the derivativeof a quotient with the numerator being 1.

Derivative of a ReciprocalExample

(not in new edition)

Higher Derivatives(page 197)

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Higher Derivatives(page 197)