Sum Rule

Definition

The Sum Rule states that the derivative of the sum of two functions is equal to the sum of their derivatives. Mathematically, if $f(x)$ and $g(x)$ are differentiable functions, then $(f+g)'(x) = f'(x) + g'(x)$.

5 Must Know Facts For Your Next Test

1. The Sum Rule only applies to functions that are differentiable over the same interval.
2. It can be extended to more than two functions: $(f+g+h)'(x) = f'(x) + g'(x) + h'(x)$.
3. The Sum Rule is a linearity property of differentiation.
4. It simplifies the process of finding derivatives when dealing with polynomial or piecewise functions.
5. The Sum Rule can be used in combination with other differentiation rules such as the Product Rule and Quotient Rule.

Review Questions

• What is the derivative of $f(x) + g(x)$ using the Sum Rule?
• How does the Sum Rule apply to three differentiable functions?
• Can you use the Sum Rule on non-differentiable functions?

Related terms

Product Rule: A rule for finding the derivative of a product of two functions: $(fg)'(x) = f'(x)g(x) + f(x)g'(x)$.

Quotient Rule: A rule for finding the derivative of a quotient of two functions: $\left( \frac{f}{g} \right)'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$.

Chain Rule: A rule for computing the derivative of a composition of two or more functions: $(f(g(x)))' = f'(g(x)) \cdot g'(x)$.