How do I find the derivative of e^y -y=x^2 -2?

Question

Do I use chain rule with -d/dy or -d/dx or dy/dx?

And then how do I find the slope of the graph if the point's at (2,0)?

Answer 1

Use implicit differentiation.

e^y -y=x^2 -2

e^y (dy/dx) - dy/dx = 2x
dy/dx( e^y - 1) = 2x
dy/dx = 2x/(e^y -1)

so for the point (2,0), dy/dx = 2(2) / (e^0 - 1)
= 4/0
this tells me that at (2,0) the tangent slope is undefined, thus the tangent will be a vertical line
The equation will be x = 2