The problem involves finding the equation of the tangent line to the implicit curve defined by the equation x^2 - xy + y^2 = 19 at the point (3, -2). The subject area pertains to implicit differentiation and the application of derivatives in the context of tangent lines.
The discussion is ongoing, with participants exploring different interpretations of the differentiation process. Some guidance has been offered regarding the use of the product rule, but there is no explicit consensus on the correct approach or resolution of the problem yet.
Participants express uncertainty about the differentiation of specific terms and the implications of their calculations on the final answer. There is a recognition of potential errors in applying the product rule, which is a key aspect of the discussion.
d(x^2)/dx= 2x and d(y^2)/dx= 2y(dy/dx) but d(-xy)/dx is NOT -dy/dx+ dy/dx!hauk-gwai said:Homework Statement
Find the equation of the tangent line to the graph of x^2 - xy + y^2 = 19 (where y=y(x)) at (3,-2).
Homework Equations
The Attempt at a Solution
So, this is what I did:
d/dx(x^2-xy+y^2) = (19)d/dx
2x*dx/dx-dy/dx+dy/dx+2y(dy/dx)=0
2x+2y(dy/dx)=0
And I am stuck, the answer to this question is:
y+2=8/7(x-3)
and I don't know how to get the slope.