Mathematical Expressions
A Appendix
Quadratic Formula
Derivatives
If ax2 + bx + c = 0, then x =
-b { 2b - 4ac 2a 2
d n du (u ) = nun - 1 dx dx
Hyperbolic Functions
d dv du (uv) = u + v dx dx dx
ex - e-x ex + e-x sinh x sinh x = , cosh x = , tanh x = 2 2 cosh x
Trigonometric Identities A C , csc u = C A B C cos u = , sec u = C B A B tan u = , cot u = B A sin2 u + cos2 u = 1
d u a b = dx v
sin u =
C
u B
sin(u { f) = sin u cos f { cos u sin f sin 2u = 2 sin u cos u cos(u { f) = cos u cos f | sin u sin f 2
2
cos 2u = cos u - sin u 1 + cos 2u 1 - cos 2u , sin u = { A 2 A 2 sin u tan u = cos u 2 1 + tan u = sec2 u 1 + cot2 u = csc2 u cos u = {
Power-Series Expansions x3 sin x = x + g 3! 2 x cos x = 1 + g 2! 682
x3 sinh x = x + + g 3! 2 x cosh x = 1 + + g 2!
A
v
du dv - u dx dx 2 v
d du (cot u) = -csc2 u dx dx d du (sec u) = tan u sec u dx dx d du (csc u) = -csc u cot u dx dx d du (sin u) = cos u dx dx d du (cos u) = -sin u dx dx d du (tan u) = sec2 u dx dx d du (sinh u) = cosh u dx dx d du (cosh u) = sinh u dx dx