differentiation of x-2
Understand the Problem
The question is asking for the derivative of the function x - 2 with respect to x. This can be solved by applying the basic rules of differentiation.
Answer
The derivative is \( 1 \).
Answer for screen readers
The derivative of the function ( x - 2 ) with respect to ( x ) is ( 1 ).
Steps to Solve
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Identify the function
The given function is ( f(x) = x - 2 ). -
Apply the differentiation rule
To differentiate the function, we apply the power rule. The power rule states that the derivative of ( x^n ) is ( nx^{n-1} ). Here, we can rewrite ( x ) as ( x^1 ).Thus,
( \frac{d}{dx}(x) = 1 ) (since ( n = 1 ))
( \frac{d}{dx}(-2) = 0 ) (since the derivative of a constant is 0). -
Combine the derivatives
Now combine the derivatives we found:
[ \frac{d}{dx}(x - 2) = \frac{d}{dx}(x) - \frac{d}{dx}(2) = 1 - 0 = 1 ]
The derivative of the function ( x - 2 ) with respect to ( x ) is ( 1 ).
More Information
The derivative represents the rate of change of the function ( f(x) = x - 2 ). In this case, the slope is constant and equal to 1, meaning that for every 1 unit increase in ( x ), ( f(x) ) increases by 1 unit.
Tips
- Ignoring the derivative of a constant: Many students forget that the derivative of a constant (like -2) is 0.
