differentiation

# differentiation - x ) =-csc 2 x Inverse Trigonometric...

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MATH 128, CALCULUS II, FALL 2011 Koray Karabina (kkarabin@uwaterloo.ca) DIFFERENTIATION RULES AND FORMULAS: Constant Rule: d dx [ c ] = 0 ( c is constant) Linearity Rule: d dx [ c 1 f ( x ) + c 2 g ( x )] = c 1 d dx [ f ( x )] + c 2 d dx [ g ( x )], ( c 1 ,c 2 are constant) Power Rule I: d dx [ x n ] = nx n - 1 ( n is any real number) Power Rule II: d dx [( g ( x )) n ] = n ( g ( x )) n - 1 d dx [ g ( x )] ( n is any real number) Product Rule: d dx [ f ( x ) g ( x )] = d dx [ f ( x )] g ( x ) + f ( x ) d dx [ g ( x )] Quotient Rule: d dx h f ( x ) g ( x ) i = d dx [ f ( x )] g ( x ) - f ( x ) d dx [ g ( x )] ( g ( x )) 2 Chain Rule: d dx [ f ( g ( x ))] = d dx ( f ( g ( x ))) d dx ( g ( x )) Trigonometric Functions d dx (sin x ) = cos x d dx (csc x ) = - (csc x )(cot x ) d dx (cos x ) = - sin x d dx (sec x ) = (sec x )(tan x ) d dx (tan x ) = sec 2 x d dx (cot
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Unformatted text preview: x ) =-csc 2 x Inverse Trigonometric Functions d dx (sin-1 x ) = 1 1-x 2 d dx (csc-1 x ) =-1 x x 2-1 d dx (cos-1 x ) =-1 1-x 2 d dx (sec-1 x ) = 1 x x 2-1 d dx (tan-1 x ) = 1 1+ x 2 d dx (cot-1 x ) =-1 1+ x 2 Logarithmic and Exponential Functions a &gt; 0 is constant, d dx ( a x ) = a x ln a d dx ( e x ) = e x d dx (log a | x | ) = 1 x ln a d dx (ln | x | ) = 1 x 1...
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