Math Problem Statement
y = (x)/(x^2 +4) find the derivative
Solution
To find the derivative of the function
we will use the quotient rule, which states that if we have a function in the form , then the derivative is given by:
Here:
- and
Let's apply the quotient rule:
Now, simplify the expression:
-
Expand the terms in the numerator:
-
Combine like terms:
So, the derivative of is:
Would you like additional details or have any questions?
Here are 5 related questions:
- How can we find the second derivative of ?
- What is the derivative of for a general constant ?
- What are the critical points of ?
- How does the derivative change if we add a constant to the numerator?
- Can we use logarithmic differentiation on this function? If so, how?
Tip: The quotient rule can be simplified by rewriting the function if possible, but it's usually best for functions with more complex denominators.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Quotient Rule
Formulas
Quotient Rule: y' = (f'(x)g(x) - f(x)g'(x)) / [g(x)]^2
Theorems
Quotient Rule
Suitable Grade Level
Grades 11-12
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