derivative of 3x - 4
Understand the Problem
The question is asking for the derivative of the function 3x - 4. To solve it, we will apply the basic rules of differentiation, specifically the power rule, which states that the derivative of x^n is n*x^(n-1).
Answer
The derivative of the function $3x - 4$ is $3$.
Answer for screen readers
The derivative of the function $3x - 4$ is $3$.
Steps to Solve
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Identify the function We have the function $f(x) = 3x - 4$.
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Differentiate each term We'll apply the power rule to differentiate each term in the function. The derivative of a constant is 0, and the derivative of $3x$ is $3 \cdot 1$ because the exponent of $x$ is 1.
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Apply the differentiation This gives us: $$ f'(x) = 3 - 0 $$
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Simplify the expression Now, simplify the expression to find the final result: $$ f'(x) = 3 $$
The derivative of the function $3x - 4$ is $3$.
More Information
The derivative represents the slope of the function at any point. Since the derivative here is a constant, it tells us that the slope of the line described by the function $3x - 4$ is consistently 3, meaning the line rises 3 units for each unit it moves to the right.
Tips
- Confusing the differentiation of a constant: Remember that the derivative of a constant is always 0.
- Not applying the power rule correctly: Ensure that when you differentiate terms like $3x$, you recognize the coefficient and the derivative of $x$.
