What is the slope of the tangent line of #ye^x-xe^(2y) = C #, where C is an arbitrary constant, at #(-2,1)#?
Apply the product rule:
To find the derivative of
Plug this back into the differentiated equation and simplify the other derivatives:
Continued simplification yields:
To find the slope of the tangent line, plug in the
The slope could be written in either form—I prefer the more exact version, but knowing the decimal equivalence can be useful for checking your answer or for a continued application.