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Basic Derivatives and Integrals Basic Trigonometry Review [sin x] dx = - cos x + C d dx [sin x] = cos x [cos x] dx = sin x + C d 2 dx [tan x] = sec x [sec x] dx = tan x + C d 2 dx [cot x] = csc x [csc ] dx = cot x + C d dx [sec x] = sec x tan x [sec x tan x] dx = sec x + C d dx [csc x] = csc x cot x [csc x cot x] dx = csc x + C d x x dx [e ] = e [e ] dx = e + C d 1 dx [ ln|x| ] = x [ 1 ] dx = ln |x| + C x Adjacent 2 2 x d -1 1 dx [ tan x ] = 1 + x2 d -1 1 dx [ sin x ] = d -1 dx [ sec x ] = e us ten po Hy 1 sin x = Opposite Hypotenuse 1 cos x = Adjacent Hypotenuse tan x = Opposite Adjacent Basic Relationships tan x = sin x cos x cot x = cos x sin x sec x = 1 cos x csc x = 1 sin x Trigonometric Identities x sin2x + cos2x = 1 tan2x + 1 = sec2x 1 -1 [ ] dx = tan x + C 2 1+x [ SOH-CAH-TOA cot2x + 1 = csc2x sin 2x = 2 sin x cos x cos 2x = cos2x - sin2x 2 cos 2x = 2 cos x - 1 cos 2x = 1 - 2sin2x sin 2x = 1 2 (1 - cos 2x) cos2x = 1 2 (1 + cos 2x) Addition Formulas -1 ] dx = sin x + C sin( a + b) = sin a cos b + cos a sin b sin( a - b) = sin a cos b - cos a sin b 1 [ -1 cos( a + b) = cos a cos b - sin a sin b ] dx = sec x + C cos( a - b) = cos a cos b + sin a sin b Mathematical Reference Formulas and Constants Quotient Rule f(x)g(x)= f'(x)g(x) + f(x)g'(x) f(x) f'(x)g(x) - f(x)g'(x) = g(x) [ g(x) ]2 Chain Rule Integration by Parts uv - Ú v du n-1 ( f(x) ) = n( f(x) ) ( f'(x)) Electron mass: 9.109 x 10-31 kg Gas Constant: 8.314 J(K-mole)-1 Electron Charge: 1.6 x 10-19 C Avogrados Number: 6.022 x 1023 Proton mass: 1.672 x 10-27 kg Grav Constant: 6.66 x 10-11 Nm2/Kg2 Permitivity Constant: 8.85 x 1012 C2/Nm2 ElectronVolt: 1.6 x 10-19 J Speed of Light: 3 x 108 m/s Brought to you by Praeter Software, for more visit http://www.praetersoftware.com More Integrals and Hyperbolics Product Rule n Opposite d dx [cos x] = - sin x Gravity: 9.8 m/s2 Speed of Sound: 344 m/s SAP: 1.013 x 105 Pascals [sin2x] dx = 12 x - 1 4 sin 2x + C sinh x = ex - e-x 2 cosh x = ex + e-x 2 tanh x = ex - e-x ex + e-x [sin3x] dx = 13 cos3x - cos x + C [cos2x] dx = 12 x + 1 4 sin 2x + C [cos3x] dx = sin x - 13 sin3x + C [tan x] dx = ln | sec x | + C [sec x] dx = ln | sec x + tan x | + C [tan2x] dx = tan x - x + C [sec2x] dx = tan x + C [ln|x|] dx = x ln|x| - x + C