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
- The constant rule applies to any real number constant.
- It simplifies differentiation when constants are involved in functions.
- The rule can be derived from the definition of the derivative as a limit.
- The constant rule is essential for combining with other differentiation rules like the sum and product rules.
- 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 $\frac{d}{dx}(3c)$?
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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 $(uv)' = u'v + uv'$.
