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It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can walk you through how to calculate the derivatives manually or answer any other related questions.

Would you like help with the steps, or do you have other questions? 

Here are five related questions to deepen your understanding:
1. What rules of differentiation are applied to power functions like \(x^n\)?
2. How do higher-order derivatives help in understanding the behavior of functions?
3. What is the significance of a fourth derivative in practical applications?
4. How would the function behave for negative or fractional exponents?
5. What happens to the function's critical points after each successive derivative?

Tip: When differentiating, always simplify the terms after each step to make further differentiation easier!

Find f', f'', f''', and f^(4) for the function f(x) = x^6 - 2x^5 + 3x + 3.

Learn how to find the first four derivatives of the polynomial function f(x) = x^6 - 2x^5 + 3x + 3. This problem covers key calculus concepts such as the power rule for differentiation. Suitable for students in Grades 11-12 or college-level calculus.

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