Common+Derivatives+and+Integrals

Common+Derivatives+and+Integrals - Common Derivatives and...

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Common Derivatives and Integrals Visit http://tutorial.math.lamar.edu for a complete set of Calculus I & II notes. © 2005 Paul Dawkins Derivatives Basic Properties/Formulas/Rules () ( ) () d c f x c fx dx ¢ = , c is any constant. () () ( ) () () f x g x fx gx ¢ ¢¢ – =– ( ) 1 nn d x nx dx - = , n is any number. 0 d c dx = , c is any constant. ( ) f g f g fg ¢ =+ (Product Rule) 2 f f g gg ¢ - = ²³ Ll (Quotient Rule) ( ) d x f gxgx dx = (Chain Rule) g x gx d dx ¢ = ee ln d d x ¢ = Common Derivatives Polynomials 0 d c dx = 1 d x dx = d c xc dx = ( ) 1 d x nx dx - = 1 d c x ncx dx - = Trig Functions ( ) si n cos d xx dx = co s sin d dx =- 2 ta n sec d dx = se c se c tan d x dx = cs c cs c cot d x dx 2 co t csc d dx Inverse Trig Functions ( ) 1 2 1 sin 1 d x dx x - = - 1 2 1 cos 1 d x dx x - - 1 2 1 tan 1 d x d - = + 1 2 1 sec 1 d x dx - = - 1 2 1 csc 1 d x dx - - 1 2 1 cot 1 d x d - + Exponential/Logarithm Functions ln d aaa dx = d dx = 1 l n ,0 d d => 1 l n d d =„ 1 lo g ln a d d x xa Hyperbolic Trig Functions ( ) sin h cosh d dx = cos h sinh d dx = 2 tan h sech d dx = sec h sec h tanh d x dx csc h csc h coth d x dx 2 cot h csch d dx
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Common Derivatives and Integrals Visit http://tutorial.math.lamar.edu for a complete set of Calculus I & II notes. © 2005 Paul Dawkins Integrals Basic Properties/Formulas/Rules ( ) ( ) c f x d x cf x dx = && , c is a constant. ( ) ( ) ( ) ( ) f x gx d x x gx dx =– & () () b b a a x F x F b Fa = =- & where ( ) ( ) F x f x dx = & bb aa c xc f x dx = , c is a constant.
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This note was uploaded on 07/19/2011 for the course STAT 314 taught by Professor Ms.tan during the Spring '11 term at University of Santo Tomas.

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Common+Derivatives+and+Integrals - Common Derivatives and...

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