Math Problem Statement
Question content area top Part 1 Find StartFraction d squared y Over dx squared EndFraction , where StartRoot y EndRootplus2xyequals1.
just give me the exact formula for what the second derivative equals
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Chain Rule
Product Rule
Quotient Rule
Second Derivative
Formulas
\( \frac{d}{dx}(\sqrt{y}) + \frac{d}{dx}(2xy) = \frac{d}{dx}(1) \)
\( \frac{dy}{dx} = \frac{-4y\sqrt{y}}{1 + 4x\sqrt{y}} \)
Quotient Rule: \( \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \cdot u' - u \cdot v'}{v^2} \)
Theorems
Chain Rule
Product Rule
Quotient Rule
Suitable Grade Level
Advanced High School or Early College Level (Grades 11-12 or College Calculus)
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