Difference between revisions of "User:Temperal/The Problem Solver's Resource9"
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*<math>\frac{df(x)\cdot g(x)}{dx}=f'(x)\cdot g(x)+ g'(x)\cdot f(x)</math> | *<math>\frac{df(x)\cdot g(x)}{dx}=f'(x)\cdot g(x)+ g'(x)\cdot f(x)</math> | ||
*<math>\frac{d\frac{f(x)}{g(x)}}{dx}=\frac{f'(x)g(x)-g'(x)f(x)}{g^2(x)}</math> | *<math>\frac{d\frac{f(x)}{g(x)}}{dx}=\frac{f'(x)g(x)-g'(x)f(x)}{g^2(x)}</math> | ||
+ | ====The Power Rule==== | ||
+ | *$\frac{dx^n}{dx}=nx^{n-1} | ||
+ | |||
===Rolle's Theorem=== | ===Rolle's Theorem=== | ||
If <math>f(x)</math> is differentiable in the open interval <math>(a,b)</math>, continuous in the closed interval <math>[a,b]</math>, and if <math>f(a)=f(b)</math>, then there is a point <math>c</math> between <math>a</math> and <math>b</math> such that <math>f'(c)=0</math> | If <math>f(x)</math> is differentiable in the open interval <math>(a,b)</math>, continuous in the closed interval <math>[a,b]</math>, and if <math>f(a)=f(b)</math>, then there is a point <math>c</math> between <math>a</math> and <math>b</math> such that <math>f'(c)=0</math> |
Revision as of 14:02, 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 Rule
Rolle's TheoremIf Extension: Mean Value TheoremIf L'Hopital's Rule
Note that this inplies that Taylor's FormulaLet
where Applications
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