Natural Logarithms

Natural Logarithms - u a u u a dx d a 1 ln 1(log log ⋅ =...

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Natural Logarithms/Exponential Functions Properties of Logarithms/Exponentials: Product Rule: x a ax ln ln ln + = Quotient Rule: x a x a ln ln ln - = Reciprocal Rule: x x ln 1 ln - = Power Rule: x n x n ln ln = a x x a x x a x a e e a x e x e a x a x a x a x x x a x ln ln ln ln 1 log ) ( log ) ln( log ln ln ln = = = = = = = = Derivative of ln x : dx du u u dx d 1 ln = Integral of 1/ u : C u du u + = ln 1 + - = + = + = + - = C u C u du u C u C u du u | csc | ln | sin | ln cot | sec | ln | cos | ln tan Derivative of dx
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Unformatted text preview: u a u u a dx d a 1 ln 1 ) (log : log ⋅ = Derivative of u e : dx du e e dx d u u = Integral of u e : ∫ + = C e du e u u Definition : If a >0 and u is a differentiable function of x, then ∫ + = = C a a du a dx du a a a dx d u u u u ln ln...
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