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

  1. Identify the function
    The given function is ( f(x) = x - 2 ).

  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).

  3. 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.
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