Math Problem Statement
what is the second derivative of \frac{-12y}{12x+2y} Calculate ๐๐ฆ๐๐ฅdydx and ๐2๐ฆ๐๐ฅ2d2ydx2 for 12๐ฅ๐ฆ+๐ฆ2=5. implicit
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Quotient Rule
Second Derivative
Formulas
\frac{dy}{dx} = \frac{-12y}{12x + 2y}
Quotient Rule: \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2}
Theorems
Implicit Differentiation Theorem
Quotient Rule
Suitable Grade Level
Grades 11-12 (Advanced Calculus)
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