3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.

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Presentation transcript:

3.3 Techniques of Differentiation Derivative 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 Power Example 7 (page 196) / 7

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 ) 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 first function times the derivative of the second plus the second times the derivative of the first.

Derivative of a Product Examples (page 194) Derivative of a product of polynomials can be done by two methods. One method is to follow the derivative of a product rule. The other method is to expand the product and then use previously presented derivative rules.

Derivative of a Product Examples (page 194)

Derivative of a Quotient (page ) The derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the denominator squared.

Derivative of a Quotient Example 6a,b (page 195)

Derivative of a Quotient Example 6b (page 195) 6b For the function in example 6, find the exact location of the horizontal tangent lines.

Derivative of a Quotient Example 6b (page 196)

Derivative of a Reciprocal (not in new edition) The derivative of the reciprocal of a function is the negative of the derivative of the function divided by the function squared. This relationship is actually an application of the derivative of a quotient with the numerator being 1.

Derivative of a Reciprocal Example (not in new edition)

Higher Derivatives (page 197) / 8

Higher Derivatives (page 197)