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What is the derivative of f(x) = 5x^4?
What is the derivative of f(x) = 5x^4?
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Practice Questions
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Q1
What is the derivative of f(x) = 5x^4?
20x^3
5x^3
15x^3
4x^3
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The derivative f'(x) = d/dx(5x^4) = 20x^3.
Questions & Step-by-step Solutions
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Q
Q: What is the derivative of f(x) = 5x^4?
Solution:
The derivative f'(x) = d/dx(5x^4) = 20x^3.
Steps: 7
Show Steps
Step 1: Identify the function you want to differentiate. In this case, the function is f(x) = 5x^4.
Step 2: Recall the power rule for derivatives. The power rule states that if you have a term in the form of ax^n, the derivative is a * n * x^(n-1).
Step 3: Apply the power rule to the term 5x^4. Here, a = 5 and n = 4.
Step 4: Multiply the coefficient (5) by the exponent (4). This gives you 5 * 4 = 20.
Step 5: Decrease the exponent by 1. The original exponent was 4, so 4 - 1 = 3.
Step 6: Combine the results from Step 4 and Step 5. The derivative is 20x^3.
Step 7: Write the final answer. The derivative f'(x) = 20x^3.
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