Common_Derivatives_Integrals_Reduced

Common_Derivatives_Integrals_Reduced - Common Derivatives...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/30/2010 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

Page1 / 2

Common_Derivatives_Integrals_Reduced - Common Derivatives...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online