The discussion focuses on the application of implicit differentiation for the curve defined by the equation x² + 3xy + y² = 5. The correct derivative, expressed as dy/dx = - (2x + 3y) / (3x + 2y), is derived through the implicit differentiation process. A participant identified an error in the initial attempt, specifically the omission of differentiating the term 3xy, which is crucial for accurate results. The final conclusion confirms the correct application of implicit differentiation techniques.
PREREQUISITESStudents studying calculus, particularly those focusing on implicit differentiation, as well as educators looking for examples of common errors in this topic.
5ymmetrica1 said:Homework Statement
For the curve x2+3xy+y2 = 5
show that [itex]\frac{dy}{dx} =- \frac{2x+3y}{3x+2y}[/itex]
Homework Equations
N.A.
The Attempt at a Solution
2x + 3xy + 2y[itex]\frac{dy}{dx}[/itex] = 0
3x + 2y [itex]\frac{dy}{dx}[/itex] = -2x+ 3y
∴ [itex]\frac{dy}{dx} =- \frac{2x+3y}{3x+2y}[/itex]
have I done this correctly?