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What is the derivative of f(x) = 3x^2 + 5x - 7?
What is the derivative of f(x) = 3x^2 + 5x - 7?
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Practice Questions
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Q1
What is the derivative of f(x) = 3x^2 + 5x - 7?
3x + 5
6x + 5
6x - 5
3x^2 + 5
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The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of f(x) = 3x^2 + 5x - 7?
Solution:
The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.
Steps: 7
Show Steps
Step 1: Identify the function you want to differentiate, which is f(x) = 3x^2 + 5x - 7.
Step 2: Recall the power rule for derivatives: if f(x) = ax^n, then f'(x) = n * ax^(n-1).
Step 3: Apply the power rule to the first term, 3x^2. The derivative is 2 * 3 * x^(2-1) = 6x.
Step 4: Apply the power rule to the second term, 5x. The derivative is 1 * 5 * x^(1-1) = 5.
Step 5: The third term, -7, is a constant. The derivative of a constant is 0.
Step 6: Combine the derivatives from Steps 3, 4, and 5. So, f'(x) = 6x + 5 + 0.
Step 7: Simplify the expression. The final derivative is f'(x) = 6x + 5.
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