Constant rule

Definition

The constant rule states that the derivative of a constant function is zero. If $c$ is a constant, then $\frac{d}{dx}c = 0$.

5 Must Know Facts For Your Next Test

1. The constant rule applies to any real number constant.
2. It simplifies differentiation when constants are involved in functions.
3. The rule can be derived from the definition of the derivative as a limit.
4. The constant rule is essential for combining with other differentiation rules like the sum and product rules.
5. Knowing this rule helps in solving more complex problems involving polynomials and other functions.

Review Questions

• What is the derivative of the function $f(x) = 7$?
• How does the constant rule help simplify finding derivatives?
• If $c$ is a constant, what is $\frac{d}{dx}(3c)$?

Related terms

Power Rule: The power rule states that if $f(x) = x^n$, then $\frac{d}{dx}x^n = nx^{n-1}$.

Sum Rule:

The sum rule states that the derivative of a sum of functions is the sum of their derivatives: $(f + g)'(x) = f'(x) + g'(x)$.

Product Rule: The product rule states that if you have two functions, $u(x)$ and $v(x)$, then their product's derivative is $(uv)' = u'v + uv'$.