I applying the difference/power rule (derivatives)

[Sentience]

Homework Statement

The problem is : take the derivative of (x - a)

Homework Equations

Power Rule : f '(x) = r x^(r-1)

Difference Rule : f '(x) = g '(x) - h '(x)

The Attempt at a Solution

This is such a simple problem but I don't understand how my solutions manual and Wolfram Alpha came to the answer. According to these sources the answer is 1.

However, because both variables in the expression are to a single power I was under the impression the derivative of each variable would equal 1, leading to (1 - 1) = 0

If you need any clarification, please let me know.

 

[hotvette]

The parameter 'a' represents a constant, not a variable. What's the derivative of a constant?

 

[cyby]

Keep in mind, x = x^1, so you can apply the power rule for this.

 

[Kevin_Axion]

If it helps, try to graph the function in your head. For instance if you have a constant, $$\beta$$, which is a straight line intersecting the y-axis. Then it becomes clear that taking the derivative or finding another function that gives the slope at each point along $$\beta$$ would definitely be $$0$$ because a horizontal line has no slope.