What is the derivative of 5x - 1?
Understand the Problem
The question is asking for the derivative of the function 5x - 1, which involves applying the rules of differentiation to find the rate of change of the function with respect to x.
Answer
The derivative is \( 5 \).
Answer for screen readers
The derivative of the function ( 5x - 1 ) is ( 5 ).
Steps to Solve
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Identify the function The given function is ( f(x) = 5x - 1 ).
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Apply the differentiation rule To find the derivative, we use the basic differentiation rule: the derivative of ( ax ) is ( a ), and the derivative of a constant is 0.
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Differentiate each term Differentiate the function term by term:
- The derivative of ( 5x ) is ( 5 ).
- The derivative of ( -1 ) is ( 0 ).
So, combining these, we have: $$ f'(x) = 5 + 0 $$
- Simplify the result Thus, the derivative simplifies to: $$ f'(x) = 5 $$
The derivative of the function ( 5x - 1 ) is ( 5 ).
More Information
The derivative represents the slope of the function at any point, and since it is a constant ( 5 ), it indicates that the function increases at a steady rate of 5 units for each unit increase in ( x ).
Tips
- Forgetting that the derivative of a constant is ( 0 ). Always ensure to apply this rule to constant terms in the function.
