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Find the derivative of the function f(x) = 3x^2 - 4x + 7
Published on October 20, 2024
Calculus
The derivative of the function f(x) = 3x^2 - 4x + 7 is f'(x) = 6x - 4.
Question
Find the derivative of f(x) = 3x^2 - 4x + 7
Answer
Let’s find the derivative of the function step-by-step.
The function is:
1. Apply the power rule:
The power rule states that the derivative of x^n is nx^(n-1). We’ll apply this to each term in the function.
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For the term 3x^2:
- n = 2, so the derivative is (2) * 3x^(2-1) = 6x
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For the term -4x:
- n = 1, so the derivative is (1) * -4x^(1-1) = -4
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For the constant term 7:
- The derivative of a constant is always 0.
2. Combine the derivatives:
The derivative of the entire function is the sum of the derivatives of each term:
Therefore, the derivative of f(x) = 3x^2 - 4x + 7 is f’(x) = 6x - 4.