calc1formulas

calc1formulas - x 2 2 bx = x b 2-b 2 Sometimes the formula...

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Some Algebra a b a c = a b + c , a b a c = a b - c ( a b ) c = a bc , a n b n = a b · n a = a 1 / 2 ; ln( a b ) = b ln a ln( ab ) = ln a + ln b , ln a b = ln a - ln b Basic Derivatives d dx x n = nx n - 1 d dx ln x = 1 x d dx e x = e x d dx sin x = cos x d dx cos x = - sin x d dx tan x = sec 2 x d dx cot x = - csc 2 x d dx sec x = sec x tan x d dx csc x = - csc x cot x d dx tan - 1 x = 1 1 + x 2 Rules for Derivatives Chain Rule, special forms: d dx ( g ( x )) n = ng ( x ) n - 1 g 0 ( x ) d dx e g ( x ) = g 0 ( x ) e g ( x ) d dx ln g ( x ) = g 0 ( x ) g ( x ) Chain Rule: d dx f ( g ( x )) = f 0 ( g ( x )) g 0 ( x ) Product Rule: d dx ( fg ) = f 0 g + fg 0 Quotient Rule: d dx ± f g = f 0 g - fg 0 g 2 Basic Integrals Z x n dx = x n +1 n + 1 + C , if n 6 = - 1 Z 1 x dx = ln | x | + C Z e x dx = e x + C Z cos xdx = sin x + C Z sin xdx = - cos x + C Z 1 1 + x 2 dx = arctan x + C Z 1 1 - x 2 dx = arcsin x + C Z sec 2 xdx = tan x + C Z sec x tan xdx = sec x + C Linear substitution If F ( x ) is an antiderivative of f ( x ), then Z f ( kx + b ) dx = 1 k F ( kx + b ) + C As in, Z cos(3 x ) dx = 1 3 sin(3 x ) + C Z 5 x + 2 dx = 1 5 (5 x + 2) 3 / 2 3 / 2 + C = ... Life Savers Complete the square:
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Unformatted text preview: x 2 + 2 bx = ( x + b ) 2-b 2 Sometimes the formula ( a ± b ) 2 = a 2 ± 2 ab + b 2 must be read backwards: a 2 ± 2 ab + b 2 = ( a ± b ) 2 To get rid of roots: ( a + b )( a-b ) = a 2-b 2 These help with trig integrals: sin 2 x = 1 2 [1-cos2 x ] cos 2 x = 1 2 [1 + cos2 x ] sin x cos x = 1 2 sin2 x And two more: ( sin 2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x...
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