What is the derivative of f(x) = 3x^4 - 5x^3 + 2x - 7?

₹0.0

Question: What is the derivative of f(x) = 3x^4 - 5x^3 + 2x - 7?

Options:

Correct Answer: 12x^3 - 15x^2 + 2

Solution:

Using the power rule, f\'(x) = 12x^3 - 15x^2 + 2.

What is the derivative of f(x) = 3x^4 - 5x^3 + 2x - 7?

What is the derivative of f(x) = 3x^4 - 5x^3 + 2x - 7?

Step 1: Identify the function f(x) = 3x^4 - 5x^3 + 2x - 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 each term in the function.
Step 4: For the first term 3x^4, the derivative is 4 * 3x^(4-1) = 12x^3.
Step 5: For the second term -5x^3, the derivative is 3 * -5x^(3-1) = -15x^2.
Step 6: For the third term 2x, the derivative is 1 * 2x^(1-1) = 2.
Step 7: For the constant term -7, the derivative is 0 because the derivative of a constant is always 0.
Step 8: Combine all the derivatives: f'(x) = 12x^3 - 15x^2 + 2.

No concepts available.