Calculus Formulas

Derivatives

f(x)	f′(x)
xⁿ	nxⁿ⁻¹
eˣ	eˣ
aˣ	aˣ ln(a)
ln(x)	1/x
sin(x)	cos(x)
cos(x)	−sin(x)
tan(x)	sec²(x)
arcsin(x)	1/√(1−x²)
arccos(x)	−1/√(1−x²)
arctan(x)	1/(1+x²)

Derivative Rules

Rule	Formula
Sum	(f+g)′ = f′+g′
Product	(fg)′ = f′g + fg′
Quotient	(f/g)′ = (f′g−fg′)/g²
Chain	(f∘g)′ = f′(g(x))·g′(x)

Integrals

∫f(x)dx	Result
∫xⁿ dx (n≠−1)	xⁿ⁺¹/(n+1) + C
∫1/x dx	ln\|x\| + C
∫eˣ dx	eˣ + C
∫sin(x) dx	−cos(x) + C
∫cos(x) dx	sin(x) + C
∫sec²(x) dx	tan(x) + C