Math Problem Statement

Find StartFraction d squared y Over dx squared EndFraction ​, where StartRoot y EndRootplusnothingxyequals1.

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Chain Rule
Product Rule
Quotient Rule
Second Derivative

Formulas

Implicit differentiation: \( \frac{d}{dx} (f(y)) = f'(y) \cdot \frac{dy}{dx} \)
Product rule: \( \frac{d}{dx}(uv) = u \frac{dv}{dx} + v \frac{du}{dx} \)
Quotient rule: \( \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \)

Theorems

Chain Rule
Product Rule
Quotient Rule

Suitable Grade Level

Grades 11-12 (Calculus level)