Math Problem Statement
Diberikan f(x) = x^5 - 4x^2 + 8. Berapakah nilai f'(1)?
Solution
The problem states:
Given , find the value of .
Solution:
-
Differentiate with respect to :
The derivative of is found by applying the power rule:
- The derivative of is .
- The derivative of is .
- The derivative of the constant is .
So,
-
Substitute into :
Simplifying,
Answer:
The value of is .
Would you like a further breakdown of each step, or do you have any other questions?
Here are five related questions for further exploration:
- What is the second derivative of ?
- How would you find for a more complex polynomial, like ?
- How does the power rule help simplify derivatives of polynomial functions?
- What is the significance of in understanding the behavior of a function?
- How would the process change if included a trigonometric term like ?
Tip: Always start by differentiating each term individually and carefully apply the power rule to each
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Power Rule
Formulas
f'(x) = nx^(n-1) for each term in polynomial differentiation
Theorems
Power Rule for Derivatives
Suitable Grade Level
Grades 11-12