What is the derivative of pi - x?
Understand the Problem
The question is asking for the derivative of the mathematical expression 'pi - x'. To solve this, we identify that the derivative of a constant (pi) is 0 and the derivative of -x is -1. Therefore, the overall derivative is 0 - 1 = -1.
Answer
-1
Answer for screen readers
The final answer is -1
Steps to Solve
- Derivative of a constant
The derivative of a constant, $ pi $, is 0 because a constant does not change and therefore its rate of change is zero.
$$ \frac{d}{dx} ( pi ) = 0 $$
- Derivative of $-x$
The derivative of $-x$ with respect to $x$ is -1 because the coefficient of $x$ (which is -1) remains as it is.
$$ \frac{d}{dx} (-x) = -1 $$
- Combine the results
Add the results from the previous steps to get the overall derivative.
$$ \frac{d}{dx} ( pi - x) = 0 - 1 = -1 $$
The final answer is -1
More Information
The pi is a constant which does not change with respect to x, hence its derivative is 0, whereas derivative of -x is simply -1.
Tips
A common mistake is forgetting that the derivative of a constant is 0, not the value of the constant itself.
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