3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant...
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Transcript of 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant...
![Page 1: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/1.jpg)
3.3 Techniques of DifferentiationDerivative of a Constant
(page 191)
The derivative of a constant function is 0.
![Page 2: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/2.jpg)
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.
![Page 3: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/3.jpg)
Derivative of x to a PowerExample 7
(page 196)
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![Page 4: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/4.jpg)
Derivative of a Constant Times a Function
(page 192)
A constant factor can be moved through a derivative sign.
![Page 5: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/5.jpg)
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.
![Page 6: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/6.jpg)
Derivatives of Sums and Differences - Examples
(page 193)
![Page 7: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/7.jpg)
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.
![Page 8: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/8.jpg)
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.
![Page 9: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/9.jpg)
Derivative of a Product Examples
(page 194)
![Page 10: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/10.jpg)
Derivative of a Product Examples
(page 194)
![Page 11: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/11.jpg)
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.
![Page 12: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/12.jpg)
Derivative of a QuotientExample 6a,b
(page 195)
![Page 13: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/13.jpg)
Derivative of a QuotientExample 6b
(page 195)
6b For the function in example 6, find the exact location of thehorizontal tangent lines.
![Page 14: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/14.jpg)
Derivative of a QuotientExample 6b
(page 196)
![Page 15: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/15.jpg)
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.
![Page 16: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/16.jpg)
Derivative of a ReciprocalExample
(not in new edition)
![Page 17: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/17.jpg)
Higher Derivatives(page 197)
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![Page 18: 3.3 Techniques of Differentiation Derivative of a Constant (page 191) The derivative of a constant function is 0.](https://reader031.fdocuments.net/reader031/viewer/2022032709/56649ed55503460f94be5d53/html5/thumbnails/18.jpg)
Higher Derivatives(page 197)
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