# 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.