3.3 techniques of differentiation derivative of a constant (page 191) the derivative of a constant...
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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)
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