Math Problem Statement
Basic Differentiation: o Differentiate the following functions with respect to x: ▪ f(x) = 3x2+2x+1
Solution
To differentiate the function with respect to , we apply the basic rules of differentiation.
Function:
Step-by-step differentiation:
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Differentiate :
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Differentiate :
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Differentiate the constant :
Final result:
The derivative of the function is .
Would you like more details on how these rules work or have any other questions?
Here are 5 related questions for further exploration:
- What is the derivative of ?
- How do we differentiate trigonometric functions like ?
- What is the second derivative of ?
- How does the chain rule apply in differentiation?
- What is the derivative of ?
Tip: When differentiating powers of , apply the power rule: .
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Math Problem Analysis
Mathematical Concepts
Differentiation
Calculus
Formulas
Power Rule: d/dx(x^n) = nx^{n-1}
Sum Rule: d/dx(f(x) + g(x)) = f'(x) + g'(x)
Theorems
Basic Differentiation Theorem
Suitable Grade Level
Grades 10-12