Question

Find an equation of the tangent line to the graph of the function at the given point.

x e^y + y e^x = 1,      (0, 1)

Answer 1

Step 1 : 

The equation is and the point is .

The slope of the tangent line is equal to the derivative of the function at .

Apply derivative on each side with respect to x. 

Step 2 :

Slope at the point :

Substitute  in  

The point-slope form of line equation is .

Substitute the point and slope in the above equation.

The tangent line equation is    

Solution : 

The tangent line equation is