Calculus Rules and Linear Approximation

Flashcards covering basic calculus rules, including the constant rule, power rule, product rule, quotient rule, and derivatives of trigonometric functions, as well as linear approximation.

Constant Rule (derivative)

d/dx (c) = 0

Power Rule

d/dx (x^n) = nx^(n-1)

Derivative of sin x

d/dx (sin x) = cos x

Derivative of cos x

d/dx (cos x) = -sin x

Product Rule

d/dx (fg) = gf’ + fg’

Quotient Rule

d/dx (f/g) = (gf' - fg') / g^2

Derivative of tan x

d/dx (tan x) = sec^2 (x)

Derivative of cot x

d/dx (cot x) = -csc^2 (x)

Derivative of sec x

d/dx (sec x) = sec x tan x

Derivative of csc x

d/dx (csc x) = -csc x cot x

Integral of sin(x)

Integral of sin(x) = -cos(x) + C

Integral of cos(x)

Integral of cos(x) = sin(x) + C

Integral of sec^2(x)

Integral of sec^2(x) = tan(x) + C

Integral of csc^2(x)

Integral of csc^2(x) = -cot(x) + C

Integral of sec(x)tan(x)

Integral of sec(x)tan(x) = sec(x) + C

Integral of $$csc(