Difference between revisions of "User:Temperal/The Problem Solver's Resource9"
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===Definition=== | ===Definition=== | ||
− | *<math>\frac{df(x)}{dx}=\lim_{x | + | *<math>\frac{df(x)}{dx}=\lim_{x\to x_0}\frac{f(x_0)-f(x)}{x_0-x}</math>, where <math>f(x)</math> is a function continuous in <math>L</math>, and <math>x_0</math> is an arbitrary constant such that <math>x_0\subset L</math>. |
*Multiple derivatives are taken by evaluating the innermost first, and can be notated as follows: <math>\frac{d^2f(x)}{dx^2}</math>. | *Multiple derivatives are taken by evaluating the innermost first, and can be notated as follows: <math>\frac{d^2f(x)}{dx^2}</math>. | ||
*The derivative of <math>f(x)</math> can also be expressed as <math>f'(x)</math>, or the <math>n</math>th derivative of <math>f(x)</math> can be expressed as <math>f^{(n)}(x)</math>. | *The derivative of <math>f(x)</math> can also be expressed as <math>f'(x)</math>, or the <math>n</math>th derivative of <math>f(x)</math> can be expressed as <math>f^{(n)}(x)</math>. | ||
+ | |||
===Basic Facts=== | ===Basic Facts=== | ||
*<math>\frac{df(x)\pm g(x)}{dx}=f'(x)\pm g'(x)</math> | *<math>\frac{df(x)\pm g(x)}{dx}=f'(x)\pm g'(x)</math> |
Revision as of 14:03, 7 October 2007
DerivativesThis page will cover derivatives and their applications, as well as some advanced limits. The Fundamental Theorem of Calculus is covered on the integral page. Definition
Basic FactsThe Power RuleRolle's TheoremIf Extension: Mean Value TheoremIf L'Hopital's Rule
Note that this inplies that Taylor's FormulaLet
where Applications
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