What is the derivative of f(x) = 5x^5 - 3x + 7? (2020)

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Question: What is the derivative of f(x) = 5x^5 - 3x + 7? (2020)

Options:

Correct Answer: 25x^4 - 3

Exam Year: 2020

Solution:

Using the power rule, f\'(x) = 25x^4 - 3.

What is the derivative of f(x) = 5x^5 - 3x + 7? (2020)

What is the derivative of f(x) = 5x^5 - 3x + 7? (2020)

Step 1: Identify the function f(x) = 5x^5 - 3x + 7.
Step 2: Recognize that we need to find the derivative, which tells us the rate of change of the function.
Step 3: Use the power rule for derivatives, which states that if f(x) = ax^n, then f'(x) = n * ax^(n-1).
Step 4: Apply the power rule to the first term, 5x^5: The derivative is 5 * 5x^(5-1) = 25x^4.
Step 5: Apply the power rule to the second term, -3x: The derivative is -3 * 1x^(1-1) = -3.
Step 6: The third term, 7, is a constant, and its derivative is 0.
Step 7: Combine the derivatives from Steps 4, 5, and 6: f'(x) = 25x^4 - 3 + 0.
Step 8: Simplify the expression: f'(x) = 25x^4 - 3.

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