# What is the slope of the tangent line of #(x-y)e^(x-y)= C #, where C is an arbitrary constant, at #(-2,1)#?

##### 2 Answers

Jul 20, 2017

#### Explanation:

Making

then

Now

and finally

Jul 20, 2017

The slope of the tangent line is

#### Explanation:

Differentiate the equation implicitly:

As

We have then two possible solutions:

#(1)" " (1 -y') = 0#

#dy/dx = 1#

#y = x + a#

or:

#(2)" "(x-y+1) = 0#

#y = x+1#

which is just the particular case of

Thus:

is the general solution, which is always a straight line of slope