What is the derivative of 1x?
Understand the Problem
The question is asking for the derivative of the function 1x, which is interpreted as the derivative of the variable x multiplied by 1. To solve it, we apply the rules of differentiation.
Answer
The derivative is \( 1 \).
Answer for screen readers
The derivative of the function ( 1x ) (or ( x )) is ( 1 ).
Steps to Solve
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Identify the function We recognize that the function is ( f(x) = 1x ). This can also be written as ( f(x) = x ) since multiplying by 1 does not change the value.
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Apply the power rule of differentiation The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). In our case, ( n = 1 ).
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Calculate the derivative Using the power rule: $$ f'(x) = 1 \cdot x^{1-1} = 1 \cdot x^0 = 1 $$
The derivative of the function ( 1x ) (or ( x )) is ( 1 ).
More Information
The derivative indicates the rate of change of a function. For a linear function like ( x ), the rate of change is constant, which is why the derivative is simply ( 1 ).
Tips
- Confusing the expression ( 1x ) with something more complex. Just recognize it simplifies to ( x ).
