Sum of functions
h(x) = f(x) + g(x)
h'(x) = f'(x) + g'(x)
Subtraction of functions
h(x) = f(x) - g(x)
h'(x) = f'(x) - g'(x)
Multiplication of functions
h(x) = f(x) • g(x)
h'(x) = f'(x) • g(x) + f(x) • g'(x)
Division of functions
h(x) = f(x) / g(x)
h'(x) = (f'(x) • g(x) - f(x) • g'(x)) / (g(x))²
The domain of f is the intersection of the domains of its component functions.
- t²: (-∞,∞)
- 1/(t+3): (-∞,-3) ∪ (-3,∞)
- √-t: -t > 0: (-∞,0]
- ln(t): t > 0: (0,∞)
- cot(t): cos(t)/sin(t): sin(t) ≠ 0: t ≠ nπ: (-∞,nπ) ∪ (nπ,∞)
- Upper triangular matrices: square matrix in which all entries below the diagonal are zeros
- Lower triangular matrices: square matrix in which all entries above the diagonal are zeros
- Diagonal matrices: matrix for which all entries above and below the diagonal are zeros