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 |