Difference between revisions of "Derivatives of Products and Quotients"
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<math> \frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} </math>. | <math> \frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} </math>. | ||
+ | |||
+ | Examples: | ||
+ | * <math> f(x) = 5x </math>, <math> g(x) = x^2 + 1 </math>. <math> f'(x) = 5 </math> and <math> g'(x) = 2x </math>, so <math> \frac{d}{dx}\left(\frac{5x}{x^2 + 1}\right) = \frac{5(x^2+1) - 5x(2x)}{(x^2 + 1)^2} = \frac{5x^2+5 - 10x^2}{(x^2 + 1)^2} = \frac{5(1 - x^2)}{(x^2 + 1)^2}</math>. | ||
+ | |||
==Resources== | ==Resources== | ||
* [http://www2.gcc.edu/dept/math/faculty/BancroftED/buscalc/chapter2/section2-4.php Product and Quotient Rules], Grover City College | * [http://www2.gcc.edu/dept/math/faculty/BancroftED/buscalc/chapter2/section2-4.php Product and Quotient Rules], Grover City College | ||
* [https://tutorial.math.lamar.edu/classes/calci/productquotientrule.aspx Product and Quotient Rule], Paul's Online Notes (Lamar University) | * [https://tutorial.math.lamar.edu/classes/calci/productquotientrule.aspx Product and Quotient Rule], Paul's Online Notes (Lamar University) |
Revision as of 12:32, 21 September 2021
Product Rule
Let and be differentiable functions. Then, the derivative of their product, , is
.
Examples:
- , . and , so .
- , . and , so .
Quotient Rule
Let and be differentiable functions such that . Then, the derivative of the quotient, , is
.
Examples:
- , . and , so .
Resources
- Product and Quotient Rules, Grover City College
- Product and Quotient Rule, Paul's Online Notes (Lamar University)