Memorize List

d/dx [cf(x)]

c’f(x)

d/dx [sinx]

cosx

d/dx [cosx]

-sinx

d/dx [f(x) + - g(x)]

f’(x) + - g’(x)

d/dx [e^x]

e^x

d/dx [tanx]

sec²x

d/dx [secx]

secxtanx

d/dx [cotx]

-csc²x

d/dx [cscx]

-cscxcotx

Continuity

Lim x→c^- f(x) = Lim x→c⁺ f(x) = f(c)

Defenition of Derivative

f’(x) = Lim Δx→0 [f(x+Δx) - f(x)] / Δx

Power rule

f(x) = xⁿ

f’(x) =nx^n-1

Average ROC

[f(b) - f(a)] / [b - a]

Average Velocity

[s(b) - s(a)] / [b - a]

Instantaneous Velocity

Lim Δt→0 [s(t+Δt] - s(t)] / Δt

Position function for free falling object

½gt² + V₀t + S₀

Product Rule

d/dx [f(x)d(x)]

f’(x)g(x) + f(x)g’(x)

Quotient Rule

d/dx [f(x) / g(x)]

[f’(x)g(x) - f(x)g’(x)] / [g(x)]²

Chain Rule

d/dx [f(g(x))]

f’(g(x)) • g’(x)

d/dx [ℓnx]

1/x

d/dx [a^x]

ℓna • a^x

T.I. [tanx]

sinx / cosx

T.I. [cscx]

1 / sinx

T.I. [secx]

1 / cosx

T.I. [cotx]

cosx / sinx

T.I. [sin²x + cos²x]

1

T.I. [sin²x]

1 - cos²x

T.I. [cos²x]

1 - sin²x

T.I. [sin(2x)]

2sinxcosx

T.I. [cos(2x)]

1 - 2sin²x

T.I. [cos(2x)]

2cos²x - 1

T.I. [cos(2x)]

cos²x - sin²x

T.I. [tan²x]

sec²x - 1

T.I. [sec²x]

tan²x + 1

d/dx [f^-1(x)]

1/ [f’(f^-1(x))]

d/dx [arcsinx]

1 / (√1-x²)

d/dx [arccosx]

-1 / (√1-x²)

d/dx [arctanx]

1 / (x²+1)

Volume of cone

V = 1/3 πr²h

Volume of sphere

V = 4/3 πr³

Volume of cylinder

V =πr²h

Volume of rectangle

V = LWH

Area of Sphere

4πr²

Circumference of circle

C = 2πr

Intermediate Value Theorem (IVT)

y-values

f(c) = k

Mean Value Theorem (MVT)

slope

f’(c) = [f(b) - f(a)] / [b-a]

Rolle’s Theorem

max/min

f’(c) = 0

∫ tanx dx

-ℓn |cosx| + c

∫ 1/x dx

ℓn |x| + c

∫ 1/cos²x dx

tanx + c

∫ xⁿ dx

xⁿ⁺¹ / n+1 + c

∫ 1 / √1-x² dx

arcsinx + c

∫ e^x dx

e^x + c

∫ 7^x dx

7^x / ℓn(7) + c

∫ cosx dx

sinx + c

∫ sinx dx

-cosx + c

∫ 1 / x² +1 dx

arctanx + c

∫ secxtanx dx

secx + c

∫ cscxcotx

-cscx + c

∫ c f(x) dx

c ∫ f(x) dx + c

Δx

(xₙ - x₀) / n

n = number of integrals

Average Value of a Function

(1 / b-a) (_a ∫ ^b f(x) dx)

Area of Semicircle

A = (πr²) / 2