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%http://www.equationsheet.com/
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Document: equationsheet.tex \LaTeXe
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Creator: Jelle de Jong
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Date: 23-11-2007
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Version: v0.1.1j
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Source: http://www.equationsheet.com/
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Algebra:
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1/6 Addition/Subtraction
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\begin{displaymath}
\textrm{1/5 Additive Identity Property }{\rm{a + 0 = a}}
\end{displaymath}
\begin{displaymath}
\textrm{2/5 Additive Inverse Property } a + \left( { - a} \right) = 0
\end{displaymath}
\begin{displaymath}
\textrm{3/5 Associative Property of Addition } \left( {a + b} \right) + c = a + \left( {b + c} \right)
\end{displaymath}
\begin{displaymath}
\textrm{4/5 Commutative Property of Addition } a + b = b + a
\end{displaymath}
\begin{displaymath}
\textrm{5/5 Definition of Subtraction } a - b = a + \left( { - b} \right)
\end{displaymath}
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2/6 Division/Multiplication
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1/6 Associative Property of Multiplication
\begin{displaymath}
\left( {a \times b} \right) \times c = a \times \left( {b \times c} \right) = a \times b \times c
\end{displaymath}
2/6 Definition of Division
\begin{displaymath}
\frac{a}{b} = a \times \left( {\frac{1}{b}} \right)
\end{displaymath}
3/6 Distributive Property
\begin{displaymath}
a\left( {b + c} \right) = ab + ac
\end{displaymath}
4/6 Multiplicative Identity
\begin{displaymath}
a \times 1 = a
\end{displaymath}
5/6 Multiplicative Inverse
\begin{displaymath}
a \times \frac{1}{a} = 1
\end{displaymath}
6/6 Zero Multiplication Property
\begin{displaymath}
a \times 0 = 0
\end{displaymath}
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3/6 Exponents/Powers
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1/9 Addition of Exponents Rule
\begin{displaymath}
x^a x^b = x^{\left( {a + b} \right)}
\end{displaymath}
2/9 Definition of Square Root
\begin{displaymath}
x^{\left( {\frac{1}{2}} \right)} = \sqrt x
\end{displaymath}
3/9 Distributive Property of Exponents
\begin{displaymath}
x^a y^a = \left( {xy} \right)^a
\end{displaymath}
4/9 Exponent Equal to One Rule
\begin{displaymath}
x^1 = x
\end{displaymath}
5/9 Exponent Equal to Zero Rule
\begin{displaymath}
x^0 = 1
\end{displaymath}
6/9 Fractional Exponent to Fractional Root Relationship
\begin{displaymath}
x^{\left( {\frac{a}{b}} \right)} = \sqrt[b]{{x^a }}
\end{displaymath}
7/9 Negative Exponent Definition
\begin{displaymath}
x^{ - a} = \frac{1}{{x^a }}
\end{displaymath}
8/9 Power Rule of Exponents
\begin{displaymath}
\left( {x^a } \right)^b = x^{\left( {ab} \right)}
\end{displaymath}
9/9 Subtraction of Exponents Rule
\begin{displaymath}
x^{\left( {a - b} \right)} = \frac{{x^a }}{{x^b }}
\end{displaymath}
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5/6 Polynomials
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1/7 Difference of Cubes Factorization
\begin{displaymath}
a^3 - b^3 = \left( {a - b} \right)\left( {a^2 + ab + b^2 } \right)
\end{displaymath}
2/7 Difference of Squares Factorization
\begin{displaymath}
a^2 - b^2 = \left( {a + b} \right)\left( {a - b} \right)
\end{displaymath}
3/7 Polynomial FOIL operation
\begin{displaymath}
\left( {a + b} \right)\left( {c + d} \right) = ac + ad + bc + bd
\end{displaymath}
4/7 Quadratic Formula
\begin{displaymath}
\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}
\end{displaymath}
5/7 Second Order Polynomial Factorization
\begin{displaymath}
x^2 + x\left( {a + b} \right) + ab = \left( {x + a} \right)\left( {x + b} \right)
\end{displaymath}
6/7 Square of a First Order Polynomial
\begin{displaymath}
\left( {a + b} \right)^2 = a^2 + 2ab + b^2
\end{displaymath}
7/7 Sum of Cubes Factorization
\begin{displaymath}
a^3 + b^3 = \left( {a + b} \right)\left( {a^2 - ab + b^2 } \right)
\end{displaymath}
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6/6 Surds
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1/3 SURD Addition and Subtraction
\begin{displaymath}
a\sqrt b \pm c\sqrt b = \left( {a \pm c} \right)\sqrt b
\end{displaymath}
2/3 SURD Division
\begin{displaymath}
\frac{{a\sqrt b }}{{c\sqrt d }} = \frac{a}{c}\sqrt {\frac{b}{d}}
\end{displaymath}
3/3 SURD Multiplication
\begin{displaymath}
a\sqrt b \times c\sqrt d = ac\sqrt {bd}
\end{displaymath}
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Calcul
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1/4 Differentiation/Differentals
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1/29 Chain Rule of Differentiation
\begin{displaymath}
\frac{d}{{dx}}\left[ {f\left( u \right)} \right] = \frac{d}{{du}}\left[ {f\left( u \right)} \right]\frac{{du}}{{dx}}
\end{displaymath}
%2/29 Definition of a Derivative
%\begin{displaymath}
%\frac{d}{{dx}}f\left( x \right) = \mathop {\lim }\limits_{\Delta \to 0} \frac{{f\left( {x + \Delta } \right) - f\left( x \right)}}{\Delta }
%\end{displaymath}
3/29 Derivative of a Constant
\begin{displaymath}
\frac{d}{{dx}}C = 0
\end{displaymath}
%4/29 Derivative of a Natural Logarithm
%\begin{displaymath}
%\frac{d}{{dx}}\ln \left( x \right) = \frac{1}{x}
%\end{displaymath}
5/29 Derivative of a Variable to the First Power
\begin{displaymath}
\frac{d}{{dx}}x = 1
\end{displaymath}
6/29 Derivative of a Variable to the nth Power
\begin{displaymath}
\frac{d}{{dx}}x^n = nx^{\left( {n - 1} \right)}
\end{displaymath}
%7/29 Derivative of an Arbitrary Base Exponential
%\begin{displaymath}
%\frac{d}{{dx}}b^x = b^x \ln \left( b \right)
%\end{displaymath}
%8/29 Derivative of an Exponential
%\begin{displaymath}
%\frac{d}{{dx}}e^{ax} = ae^{ax}
%\end{displaymath}
%9/29 Derivative of Cosecant
%\begin{displaymath}
%\frac{d}{{dx}}\csc x = - \csc x\cot x
%\end{displaymath}
%10/29 Derivative of Cosine
%\begin{displaymath}
%\frac{d}{{dx}}\cos x = - \sin x
%\end{displaymath}
28/29 Product Rule of Differentiation
\begin{displaymath}
\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)
\end{displaymath}
29/29 Quotient Rule of Differentiation
\begin{displaymath}
\frac{d}{{dx}}\left( {\frac{{f\left( x \right)}}{{g\left( x \right)}}} \right) = \frac{{\frac{d}{{dx}}f\left( x \right)g\left( x \right) - f\left( x \right)\frac{d}{{dx}}g\left( x \right)}}{{g^2 \left( x \right)}}
\end{displaymath}
\end{document}