The discussion focuses on using implicit differentiation to find dy/dx for the equation y - sin(xy) = x^2. The correct differentiation process involves applying the chain rule and product rule, leading to the equation dy/dx * (y - cos(xy)(x)) = 2x + cos(xy)(y). Participants emphasize the importance of correctly differentiating y, noting that \(\frac{d}{dx}(y) \neq \frac{dy}{dx}y\). The final step requires grouping like terms and factoring out dy/dx to isolate it.
PREREQUISITESStudents studying calculus, particularly those learning about implicit differentiation, and educators seeking to clarify common mistakes in differentiation techniques.
suchgreatheig said:Homework Statement
Use implicit differentiation to find dy/dx if y - sin(xy) = x^2.