Math Problem Statement
Теорема про похідну частки функцій \( \left( \frac{u}{v} \right)' \).
Solution
This text is written in Ukrainian and refers to the theorem for the derivative of the quotient of functions. The expression in parentheses represents the derivative of the quotient .
The rule for the derivative of a quotient is given by the quotient rule in calculus:
where:
- and are differentiable functions of ,
- is the derivative of ,
- is the derivative of ,
- to ensure the denominator is non-zero.
Would you like me to explain how this rule is derived or provide an example?
Related Questions:
- What is the product rule for derivatives, and how does it relate to the quotient rule?
- How do you apply the quotient rule to trigonometric functions, such as ?
- Can you demonstrate the quotient rule using an example with polynomials?
- What happens if the denominator equals zero in the quotient rule?
- How does the quotient rule extend to higher-order derivatives?
Tip: Always check that the denominator in the quotient rule does not equal zero to avoid undefined expressions.
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Quotient Rule
Formulas
(u/v)' = (u'v - uv') / v^2
Theorems
Quotient Rule for Derivatives
Suitable Grade Level
Grades 11-12 / Early University