Common_Derivatives_Integrals

Common_Derivatives_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 cf x cf x dx = , c is any constant. () () fx gx f x gx ′′ ±= ± 1 nn d xn x dx = , n is any number. 0 d c dx = , c is any constant. fg f g fg =+ (Product Rule) 2 ff g f g gg ⎛⎞ = ⎜⎟ ⎝⎠ (Quotient Rule) d fgx f gx gx dx = (Chain Rule) gx d dx = ee ( ) ln d dx g x = Common Derivatives Polynomials 0 d c dx = 1 d x dx = d cx c dx = 1 d x dx = 1 d cx ncx dx = Trig Functions sin cos d xx dx = cos sin d dx =− 2 tan sec d dx = sec sec tan d x dx = csc csc cot d x dx 2 cot 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 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 dx = cosh sinh d dx = 2 tanh sech d dx = sech sech tanh d x dx csch csch coth d x dx 2 coth 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 () () cf x dx c f x dx = ∫∫ , c is a constant. ( ) ( ) ( )( ) f x g x dx f x dx g x dx ±= ± b b a a fxd x Fx Fb Fa == where ( ) ( ) Fx x = bb aa cf x dx c f x dx = , c is a constant. () () () () b a f x g x dx f x dx g x dx ± () 0 a a x = ba ab x x =− () () () bcb aac x x x =+ ∫∫∫ b a cdx c b a If 0 fx on axb ≤≤ then 0 b a x If fx gx
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Common_Derivatives_Integrals - Common Derivatives and...

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