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Mathematics Formula Sheet
Calculus · Trigonometry · Algebra · Statistics
Calculus
Trigonometry
Algebra
Statistics
Linear Algebra
Derivatives
Power Rule
d/dx [x
n
] =
n
x
n−1
Product Rule
d/dx [
uv
] =
u
'
v
+
uv
'
Quotient Rule
d/dx [
u
/
v
] = (
u
'
v
−
uv
') /
v
2
Chain Rule
d/dx [f(g(x))] = f'(g(x)) · g'(x)
d/dx [sin x]
cos x
d/dx [cos x]
−sin x
d/dx [tan x]
sec
2
x
d/dx [eˣ]
e
x
d/dx [ln x]
1 / x
Integrals
Power Rule
∫ x
n
dx = x
n+1
/(n+1) + C
∫ sin x dx
−cos x + C
∫ cos x dx
sin x + C
∫ eˣ dx
e
x
+ C
∫ 1/x dx
ln |x| + C
∫ sec²x dx
tan x + C
Substitution
∫ f(g(x))g'(x)dx = ∫ f(u)du
By Parts
∫ u dv = uv − ∫ v du
FTC
∫
a
b
f(x)dx = F(b) − F(a)
Trigonometry
Click θ four times
Pythagorean
sin²
θ
+ cos²
θ
= 1
Double Angle
sin(2
θ
) = 2sin
θ
cos
θ
cos Double
cos(2
θ
) = cos²
θ
− sin²
θ
Sum Formula
sin(A+B) = sinA cosB + cosA sinB
Law of Sines
a/sin A = b/sin B = c/sin C
Law of Cosines
c² = a² + b² − 2ab cos C
Euler's Formula
e
i
θ
= cos
θ
+ i·sin
θ
Limits & Series
L'Hôpital
lim f/g = lim f'/g' (0/0 form)
Taylor Series
f(x) = Σ f
(n)
(a)(x−a)
n
/n!
Geometric
Σ ar
n
= a/(1−r), |r|<1
Squeeze Thm
g≤f≤h ∧ lim g=lim h=L ⟹ lim f=L
sin x / x
lim
x→0
sin x / x = 1