math reference formula

Here is the list of the calculus formula. hope it will help you in your work.^_^



Reminder : If x^.5 ,in words it is the square root of x.

A) DIFFERENTIATION FORMULAS	Note : c=constant, f and g are functions 1) (cf)' = cf' 2) (f+g)' = f'+g' 3) (f-g)' = f'-g' 4) (fg)' = f'g+fg' 5) (f/g)' = (f'g-fg')/g^2 6) (d/dx)(x^n) = nx^(n-1) 7) (d/dx)c = 0
B) DIFFERENTIATION of TRIGONOMETRIC FUNCTIONS	1) (d/dx) sin x = cos x 2) (d/dx) cos x = -sin x 3) (d/dx) tan x = sec^2(x) 4) (d/dx) csc x = -csc x cot x 5) (d/dx) sec x = sec x tan x 6) (d/dx) cotx = -csc^2(x)
C) TRIGONOMETRIC IDENTITIES	1) sin^2(x)+cos^2(x) = 1 2) tan^2(x)+1 = sec^2(x) 3) cot^2(x)+1 = csc^2(x) 4) tan x = sin x / cos x 5) cot x = cos x / sin x 6) csc x = 1 / sin x 7) secx = 1 / cos x 8) cot x = 1 / tan x Addition Formulas: 9) sin(x+y) = sin x cos y + cos x sin y 10) cos(x+y) = cos x cos y - sin x sin y 11) tan(x+y) = (tan x + tan y) / (1-tan x tan y) Subtraction Formulas: 12) sin(x-y) = sin x cos y - cos x sin y 13) cos(x-y) = cos x cos y + sin x sin y 14) tan(x-y) = (tan x - tan y) / (1+tan x tan y) Double Angle Formulas: 15) sin 2x = 2sin x cos x 16) cos 2x = cos^2(x)-sin^2(x) 17) cos 2x = 2cos^2(x)-1 18) cos 2x = 1-2sin^2(x) Half Angle Formulas: 19) cos^2(x) = (1+cos 2x) / 2 20) sin^2(x) = (1-cos 2x) / 2 Product Formulas: 21) sin x cos y = [sin (x+y)+sin (x-y)] / 2 22) cos x cos y = [cos (x+y)+cos (x-y)] / 2 23)sin x sin y = [cos (x-y)-cos (x+y)] / 2
D) QUADRATIC EQUATION	for ax^2+bx+c = 0 x = [-b(+or-)(b^2-4ac)^.5] / 2a
E) BASIC INTEGRAL FORMS	1) ƒudv = uv-ƒvdu 2) ƒu^n du = (1 / (n+1))u^(n+1)+C 3) ƒdu/u = ln|u|+C 4) ƒe^u du = e^u+C 5) ƒa^u du = (1 / (lna))a^u+C 6) ƒsin udu = -cos u +C 7) ƒcos udu = sin u+C 8) ƒsec^2(u)du = tan u+C 9) ƒcsc^2(u)du = -cot u+C 10) ƒsec u tan udu = sec u+C 11) ƒcsc u cot udu = -csc u+C 12) ƒtan udu = ln|sec u|+C 13) ƒcot udu = ln|sin u|+C 14) ƒsec udu = ln|sec u+tan u|+C 15) ƒcsc udu = ln|csc u-cot u|+C 16) ƒdu/(a^2-u^2)^.5 = [sin^-1(u / a)]+C 17) ƒdu/(a^2+u^2) = [(tan^-1(u / a)) / a]+C 18) ƒdu/[u(u^2-a^2)^.5] = [(sec^-1(u / a)) / a]+C 19) ƒdu/(a^2-u^2) = [ln|(u+a) / (u-a)|] / 2a+C 20) ƒdu/(u^2-a^2) = [ln|(u-a) / (u+a)|] / 2a+C
F) TRIGONOMETRIC INTEGRAL FORMS	21) ƒsin^2(u)du = (u / 2)-(sin 2u) / (2u)+C 22) ƒcos^2(u)du = (u / 2)+(sin 2u) / (2u)+C 23) ƒtan^2(u)du = tan u -u+C 24) ƒcot^2(u)du = -cot u -u+C 25) ƒsin^3(u)du = -[{2+sin^2(u)}cos u / 3]+C 26) ƒcos^3(u)du = [{2+cos^2(u)}sin u / 3]+C 27) ƒtan^3(u)du = [{tan^2(u)} / 2]+ln|cos u|+C 28) ƒcot^3(u)du = -[(cot^2(u)] / 2 - ln|sin u|+C 29) ƒsec^3(u)du = [(sec u tan u ) / 2]+[(ln|sec u + tan u|) / 2]+C 30) ƒcsc^3(u)du = -[(csc u cot u) / 2]+[(ln|csc u - cot u|) / 2]+C 31) ƒusin u du = sin u -ucos u+C 32) ƒucos udu = cos u + usin u+C
G) EXPONENTIAL and LOGARITHMIC INTEGRAL FORMS	33) ƒue^(au)du = [(au-1) / a^2]e^(au)+C 34) ƒ(u^n)(e^au)du = {[(u^n)(e^au)] / a} - (n / a)ƒ[u^(n-1)](e^au)du 35) ƒ(e^au)sin bu du = [(e^au) / (a^2+b^2)](asin bu-bcos bu)+C 36) ƒ(e^au)cos bu du = [(e^au) / (a^2+b^2)](acos bu+bsin bu)+C 37) ƒln udu = uln u-u+C 38) ƒ(u^n)ln udu = [(u^(n+1)) / (n+1)^2][(n+1)(ln u-1)]+C 39) ƒdu / (uln u) = ln|ln u|+C
H) HYPERBOLIC INTEGRAL FORMS	40) ƒsinh udu = cosh u+C 41) ƒcosh udu = sinh u+C 42) ƒtanh udu = lncosh u+C 43) ƒcoth udu = ln|sinh u|+C 44) ƒsech udu = tan^-1|sinh u|+C 45) ƒcsch udu = ln|tan(u / 2)|+C 46) ƒsech^2(u)du = tanh u+C 47) ƒcsch^2(u)du = -coth u+C 48) ƒsech utanh udu = -sech u+C 49) ƒcsch ucoth udu = -csch u+C
I) COORDINATE CONVERSION FORMULAS	θ = theta , φ = phi From Cylindrical to Rectangular x = rcos θ y = rsin θ z = z From Rectangular to Cylindrical r = (x^2 + y^2)^.5 tan θ = y / x z = z From Spherical to Rectangular x = psin φ cos θ y = psin φ sin θ z = pcos φ From Rectangular to Spherical p = (x^2 + y^2 + z^2)^.5 φ = cos^-1(z / p) cos θ = x / (psin φ) sin θ = y / (psin φ)