What is the slope of the tangent line of #ye^x-xe^(2y) = C #, where C is an arbitrary constant, at #(-2,1)#?
1 Answer
Explanation:
Apply the product rule:
To find the derivative of
Plug this back into the differentiated equation and simplify the other derivatives:
Solve for
Continued simplification yields:
To find the slope of the tangent line, plug in the
Simplify:
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.