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What is the derivative of f(x) = x^5?
What is the derivative of f(x) = x^5?
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Practice Questions
1 question
Q1
What is the derivative of f(x) = x^5?
5x^4
4x^5
x^4
5x^3
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The derivative f'(x) = d/dx(x^5) = 5x^4.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of f(x) = x^5?
Solution:
The derivative f'(x) = d/dx(x^5) = 5x^4.
Steps: 6
Show Steps
Step 1: Identify the function you want to differentiate. In this case, the function is f(x) = x^5.
Step 2: Use the power rule for differentiation. The power rule states that if you have x raised to a power n, the derivative is n * x^(n-1).
Step 3: Apply the power rule to f(x) = x^5. Here, n = 5.
Step 4: Multiply the exponent (5) by the coefficient (which is 1 for x^5) to get 5.
Step 5: Decrease the exponent by 1. So, 5 - 1 = 4.
Step 6: Combine the results from Step 4 and Step 5. This gives you the derivative: f'(x) = 5x^4.
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