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 cf x cf x dx = , c is any constant. () () f xg x fxg x ′′ ±= ± 1 nn d x nx dx = , n is any number. 0 d c dx = , c is any constant. f gf g f g =+ (Product Rule) 2 f fg fg gg ⎛⎞ = ⎜⎟ ⎝⎠ (Quotient Rule) d f gx f gx g x dx = (Chain Rule) g x d gx dx = ee ( ) ln g x d dx g x = Common Derivatives Polynomials 0 d c dx = 1 d x dx = d cx c dx = 1 d x nx dx = 1 d cx ncx dx = Trig Functions sin cos d x x dx = cos sin d x x dx =− 2 tan sec d x x dx = sec sec tan d x xx dx = csc csc cot d x dx 2 cot csc d x x 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 dx x = + 1 2 1 sec 1 d x dx = 1 2 1 csc 1 d x dx 1 2 1 cot 1 d x dx x + Exponential/Logarithm Functions ln d aaa dx = d dx = 1 ln , 0 d dx x => 1 ln , 0 d dx x =≠ 1 log , 0 ln a d dx x a Hyperbolic Trig Functions sinh cosh d x x dx = cosh sinh d x x dx = 2 tanh sech d x x dx = sech sech tanh d x dx csch csch coth d x dx 2 coth csch d x x 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 ( ) ( ) cf x dx c f x dx = , c is a constant. ( ) ( ) ( ) ( ) f x gxd x f xd x gxd x ± ∫∫ b b a a x Fx Fb Fa == where ( ) ( ) Fx fxd x = bb aa cf x dx c f x dx = , c is a constant.
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Common_Derivatives_Integrals_Reduced - Common Derivatives...

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