What is the derivative of x - 3?
Understand the Problem
The question is asking for the derivative of the function f(x) = x - 3 with respect to x. This will involve applying the basic rules of differentiation.
Answer
1
Answer for screen readers
The final answer is 1
Steps to Solve
- Apply the power rule for differentiation
The power rule states that for any function $f(x) = x^n$, the derivative $f'(x) = nx^{n-1}$. For $x^{-1}$.
$$\text{d}(x) / \text{d}x = 1$$
- Differentiate the constant term
The derivative of any constant is 0.
$$\text{d}(-3) / \text{d}x = 0$$
- Combine results
The derivative of $f(x) = x - 3$ is then:
$$f'(x) = 1 + 0 = 1$$
The final answer is 1
More Information
The slope of the function $f(x) = x - 3$ is constant, and equal to 1
Tips
A common mistake when finding derivatives is forgetting to apply the rule that the derivative of a constant is always zero.