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What is the derivative of f(x) = 5x^4 - 3x + 2?
What is the derivative of f(x) = 5x^4 - 3x + 2?
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Q1
What is the derivative of f(x) = 5x^4 - 3x + 2?
20x^3 - 3
20x^3 + 3
15x^3 - 3
5x^3 - 3
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The derivative f'(x) = d/dx(5x^4 - 3x + 2) = 20x^3 - 3.
Questions & Step-by-step Solutions
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Q
Q: What is the derivative of f(x) = 5x^4 - 3x + 2?
Solution:
The derivative f'(x) = d/dx(5x^4 - 3x + 2) = 20x^3 - 3.
Steps: 7
Show Steps
Step 1: Identify the function f(x) = 5x^4 - 3x + 2.
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 the first term 5x^4: The derivative is 4 * 5x^(4-1) = 20x^3.
Step 4: Apply the power rule to the second term -3x: The derivative is 1 * -3x^(1-1) = -3.
Step 5: The third term is a constant (2), and the derivative of a constant is 0.
Step 6: Combine the derivatives from Steps 3, 4, and 5: f'(x) = 20x^3 - 3 + 0.
Step 7: Simplify the expression: f'(x) = 20x^3 - 3.
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