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Q1. What is the derivative of f(x) = x^4 + 2x^3 - x + 1? (2017)
Solution:
The derivative f'(x) = d/dx(x^4 + 2x^3 - x + 1) = 4x^3 + 6x^2 - 1.
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Q2. Find the derivative of f(x) = x^5 - 3x^3 + 2. (2022)
Solution:
The derivative f'(x) = d/dx(x^5 - 3x^3 + 2) = 5x^4 - 9x^2.
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Q3. What is the derivative of f(x) = 3x^2 + 5x - 7? (2021) 2021
Solution:
The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.
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Q4. Find the derivative of f(x) = tan(x). (2022) 2022
Solution:
The derivative f'(x) = d/dx(tan(x)) = sec^2(x).
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Q5. Find the derivative of f(x) = sin(x) + cos(x).
Solution:
The derivative f'(x) = d/dx(sin(x) + cos(x)) = cos(x) - sin(x).
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Q6. Calculate the derivative of f(x) = x^2 * e^x. (2023) 2023
Solution:
Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x(2x + 1).
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Q7. Calculate the derivative of f(x) = ln(x^2 + 1).
Solution:
Using the chain rule, f'(x) = d/dx(ln(x^2 + 1)) = (2x)/(x^2 + 1).
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Q8. What is the derivative of f(x) = 5x^4?
Solution:
The derivative f'(x) = d/dx(5x^4) = 20x^3.
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Q9. What is the derivative of f(x) = x^3 - 4x?
Solution:
The derivative f'(x) = d/dx(x^3 - 4x) = 3x^2 - 4.
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Q10. What is the derivative of f(x) = 1/x?
Solution:
The derivative f'(x) = d/dx(1/x) = -1/x^2.
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