Math Problem Statement
Solution
To solve the problem of finding the derivative for the given function :
Step 1: Differentiate each term of
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The first term is . The derivative is found using the power rule .
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The second term is . The derivative of is 1.
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The third term is a constant . The derivative of a constant is 0.
Step 2: Combine the derivatives
Step 3: Compare with the given options
The correct answer is C. .
Would you like more details on any step or have any questions? Here are some related questions you might be interested in:
- What is the power rule for differentiation?
- How do you differentiate a constant?
- How do you apply the derivative rules to functions with multiple terms?
- What is the general rule for differentiating ?
- How do you handle negative exponents in differentiation?
- How do you differentiate polynomial functions?
- What is the importance of simplifying after differentiation?
- How does the chain rule differ from the power rule in differentiation?
Tip: When differentiating polynomials, always apply the power rule term by term and combine the results.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Power Rule
Derivative of Constants
Polynomial Functions
Formulas
Power rule for differentiation: \( \frac{d}{dx}[x^n] = n \cdot x^{n-1} \)
Theorems
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Suitable Grade Level
High School