CHEAT SHEET
DERIVATIVES
Constant: d/dx c = 0
Power: d/dx xⁿ = nxⁿ⁻¹
Sin: d/dx sin(x) = cos(x)
Cos: d/dx cos(x) = −sin(x)
Exponential: d/dx bˣ = bˣ · ln(b)
Logarithm: d/dx ln(x) = 1/x
INTEGRALS
Power: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)
Log: ∫x⁻¹ dx = ln|x| + C
Exp (e): ∫eˣ dx = eˣ + C
Exp (a): ∫aˣ dx = aˣ / ln(a) + C
Const. Multiple: ∫kf(x) dx = k·∫f(x) dx
Abs. Value: ∫|x| dx = x|x|/2 + C
Sum: ∫[f+g] dx = ∫f dx + ∫g dx
Difference: ∫[f−g] dx = ∫f dx − ∫g dx
LIMITS
Sum: lim(f+g) = lim f + lim g
Difference: lim(f−g) = lim f − lim g
Const. Multiple: lim(cf) = c · lim f
Product: lim(fg) = lim f · lim g
Quotient: lim(f/g) = lim f / lim g (lim g ≠ 0)
Power: lim [f(x)]ⁿ = [lim f(x)]ⁿ
Root: lim ⁿ√f(x) = ⁿ√(lim f(x))
Constant: lim c = c
Direct Substitution: lim(x→a) f(x) = f(a) when f is continuous at a
