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Find the derivative of f(x) = x^5 - 3x + 2.
Find the derivative of f(x) = x^5 - 3x + 2.
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Practice Questions
1 question
Q1
Find the derivative of f(x) = x^5 - 3x + 2.
5x^4 - 3
5x^4 + 3
4x^3 - 3
5x^4 - 2
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The derivative f'(x) = d/dx(x^5) - d/dx(3x) + d/dx(2) = 5x^4 - 3.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the derivative of f(x) = x^5 - 3x + 2.
Solution:
The derivative f'(x) = d/dx(x^5) - d/dx(3x) + d/dx(2) = 5x^4 - 3.
Steps: 8
Show Steps
Step 1: Identify the function you want to differentiate, which is f(x) = x^5 - 3x + 2.
Step 2: Break down the function into three parts: x^5, -3x, and +2.
Step 3: Differentiate each part separately using the power rule and basic derivative rules.
Step 4: For the first part, x^5, apply the power rule: bring down the exponent (5) and reduce the exponent by 1. This gives you 5x^(5-1) = 5x^4.
Step 5: For the second part, -3x, the derivative is simply -3 because the derivative of x is 1.
Step 6: For the third part, +2, the derivative is 0 because the derivative of a constant is 0.
Step 7: Combine the results from Steps 4, 5, and 6: f'(x) = 5x^4 - 3 + 0.
Step 8: Simplify the expression to get the final derivative: f'(x) = 5x^4 - 3.
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