Check request: Implicit Differentiation

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SUMMARY

The discussion focuses on finding the derivative dy/dx using implicit differentiation for the equation x² + xy = 5. The solution involves substituting x = 2 and solving for y, which results in y = 1/2. The derivative is calculated using the formula dy/dx = (-2x - y) / x, leading to the final result of dy/dx = -9/4 when x = 2.

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  • Understanding of implicit differentiation
  • Familiarity with basic algebraic manipulation
  • Knowledge of derivatives and their notation
  • Ability to substitute values into equations
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  • Study the concept of implicit differentiation in calculus
  • Practice solving similar problems involving derivatives of implicit functions
  • Explore applications of derivatives in real-world scenarios
  • Learn about higher-order derivatives and their significance
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Students studying calculus, particularly those focusing on derivatives and implicit differentiation techniques.

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Homework Statement


Find the value of dy/dx at x=2 when

x2+xy=5

The Attempt at a Solution



To find y:
22+2y=5
y=1/2

To find dy/dx:
2x(dx/dx)+x(dy/dx)+y(dx/dx)=0

2x+x(dy/dx)+y=0

(dy/dx)=(-2x-y) / x

Plug in y and x:
dy/dx=-2(2)-(1/2) / 2

dy/dx=-9/4 when x=2
 
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Correct.
 

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