What is the derivative of f(x) = 3x^2 + 5x - 7? (2021) 2021

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Question: What is the derivative of f(x) = 3x^2 + 5x - 7? (2021) 2021

Options:

Correct Answer: 6x + 5

Exam Year: 2021

Solution:

The derivative f\'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.

What is the derivative of f(x) = 3x^2 + 5x - 7? (2021) 2021

What is the derivative of f(x) = 3x^2 + 5x - 7? (2021) 2021

Step 1: Identify the function f(x) = 3x^2 + 5x - 7.
Step 2: Recall the power rule for derivatives: d/dx(x^n) = n*x^(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 derivative of the constant term -7 is 0, since constants do not change.
Step 6: Combine the results from Steps 3, 4, and 5: f'(x) = 6x + 5 + 0.
Step 7: Write the final answer: f'(x) = 6x + 5.

No concepts available.