Math Problem Statement
Find the derivative of the function. y = 3 √x + 6
Solution
To find the derivative of the function , we need to apply the rules of differentiation.
The function can be rewritten as:
Now, we'll differentiate term by term:
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The derivative of with respect to is:
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The derivative of the constant is:
So, the derivative of the function is:
This can also be expressed as:
Would you like any additional details or have any questions? Here are five related questions you might consider:
- What is the second derivative of ?
- How does the derivative behave as approaches zero?
- What is the slope of the function at a specific point, say ?
- How would you integrate to find the original function?
- Can you explore the concavity of the function using the second derivative?
Tip: Always remember that constants like 6 in differentiation disappear because the rate of change of a constant is zero.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Power rule
Constant rule
Formulas
Power rule of differentiation
Theorems
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Suitable Grade Level
Advanced High School / College