What is the derivative of f(x) = 3x^4 - 5x^2 + 2? (2021)

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Question: What is the derivative of f(x) = 3x^4 - 5x^2 + 2? (2021)

Options:

Correct Answer: 12x^3 - 10x

Exam Year: 2021

Solution:

Using the power rule, f\'(x) = 12x^3 - 10x.

What is the derivative of f(x) = 3x^4 - 5x^2 + 2? (2021)

What is the derivative of f(x) = 3x^4 - 5x^2 + 2? (2021)

Step 1: Identify the function f(x) = 3x^4 - 5x^2 + 2.
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 each term in the function:
- For the first term 3x^4: The derivative is 4 * 3x^(4-1) = 12x^3.
- For the second term -5x^2: The derivative is 2 * -5x^(2-1) = -10x.
- For the constant term 2: The derivative is 0 because the derivative of a constant is always 0.
Step 5: Combine the derivatives of all terms: f'(x) = 12x^3 - 10x + 0.
Step 6: Simplify the expression: f'(x) = 12x^3 - 10x.

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