Find the derivative of f(x) = 5x^2 + 3x - 7. (2020)

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Question: Find the derivative of f(x) = 5x^2 + 3x - 7. (2020)

Options:

Correct Answer: 10x + 3

Exam Year: 2020

Solution:

Using the power rule, f\'(x) = 10x + 3.

Find the derivative of f(x) = 5x^2 + 3x - 7. (2020)

Find the derivative of f(x) = 5x^2 + 3x - 7. (2020)

Step 1: Identify the function f(x) = 5x^2 + 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^2: The derivative is 2 * 5 * x^(2-1) = 10x.
Step 5: Apply the power rule to the second term 3x: The derivative is 1 * 3 * x^(1-1) = 3.
Step 6: The derivative of the constant term -7 is 0, since constants do not change.
Step 7: Combine the results from steps 4, 5, and 6: f'(x) = 10x + 3 + 0.
Step 8: Simplify the expression: f'(x) = 10x + 3.

Power Rule – The power rule states that the derivative of x^n is n*x^(n-1).
Polynomial Derivatives – Finding the derivative of polynomial functions involves applying the power rule to each term.