Math Problem Statement
2π₯ 2 +5π₯+3 π₯+9 diff wrt x
Solution
To differentiate the expression with respect to , we will use the quotient rule. The quotient rule states that if we have a function , then its derivative is given by:
Here, we have:
Now, let's differentiate and :
Using the quotient rule:
Now we expand and simplify:
Expanding both terms:
Now subtract :
Simplifying the numerator:
So, the derivative of the function is:
Would you like more details or further clarifications?
Here are 5 related questions:
- How is the quotient rule applied to more complex functions?
- What other methods can be used to differentiate rational functions?
- Can this differentiation be solved using implicit differentiation?
- How do higher-order derivatives of rational functions behave?
- What is the significance of critical points in such rational functions?
Tip: The quotient rule is particularly useful for differentiating rational functions where both the numerator and denominator involve . Always apply it carefully to avoid mistakes in expanding terms.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Quotient Rule
Formulas
f'(x) = (v(x) * u'(x) - u(x) * v'(x)) / (v(x))^2
Derivative of u(x) = 4x + 5
Derivative of v(x) = 1
Theorems
Quotient Rule for Differentiation
Suitable Grade Level
Undergraduate Calculus
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