What is the derivative of f(x) = 3x^2 + 5x - 7?
Correct Answer: f'(x) = 6x + 5
- 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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