Definiciones
Storyboard
Bases para comprender como se deriva e integra para comprender como en física se resuelven ecuaciones que se formulan con derivadas.
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Changing Variables on the Derivative
Equation
$\displaystyle\frac{df}{dx}=\displaystyle\frac{df}{du}\displaystyle\frac{du}{dx}$
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Constant by a Function
Equation
$\farc{\partial}{\partial x}(cf)=c\farc{\partial f}{\partial x}$
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Definition of the Derivative
Equation
$\displaystyle\frac{df}{dx}=\lim_{\epsilon\rightarrow 0}\displaystyle\frac{f(x+\epsilon)-f(x)}{\epsilon}$
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Definition of the Derivative Partial
Equation
$\displaystyle\frac{\partial f}{\partial x_i}=\lim_{\epsilon\rightarrow 0}\displaystyle\frac{f(x_1,x_2,\ldots,x_i+\epsilon,\ldots,x_n)-f(x_1,x_2,\ldots,x_i+\epsilon,\ldots,x_n)}{\epsilon}$
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Derivative of the Divisions Functions
Equation
$\displaystyle\displaystyle\frac{d}{dx}\left(\displaystyle\displaystyle\frac{f}{g}\right)=\displaystyle\displaystyle\frac{\displaystyle\displaystyle\frac{df}{dx}g - f\displaystyle\displaystyle\frac{dg}{dx}}{g^2}$
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Product Features
Equation
$\farc{\partial}{\partial x}(fg)=\farc{\partial f}{\partial x}g+f\farc{\partial g}{\partial x}$
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Sum of Functions
Equation
$\farc{\partial}{\partial x}(f+g)=\farc{\partial f}{\partial x}+\farc{\partial g}{\partial x}$
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