Common_Derivatives_Integrals_Reduced

# Common_Derivatives_Integrals_Reduced - Common Derivatives...

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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 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 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. () () () () b a f x x x ´ 0 a a = ´ ba ab x () () () bcb a ac x x ´´´ ( ) b a cd x cba ´ If ( ) 0 on axb ££ then 0 b a ´ If ( ) ( ) f x on then x Common Integrals

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Common_Derivatives_Integrals_Reduced - Common Derivatives...

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