13-26 Implicit differentiation Carry out the following steps.
a. Use implicit differentiation to find dy/dx.
x = e^y; (2, ln 2)

Verified step by step guidance

1. Start with the given equation x = e^y and differentiate both sides with respect to x, remembering that y is a function of x.
2. Apply the chain rule on the right side: the derivative of e^y with respect to x is e^y * (dy/dx).
3. Set up the equation from the differentiation: 1 = e^y * (dy/dx).
4. Solve for dy/dx by isolating it on one side of the equation: dy/dx = 1 / e^y.
5. Substitute the point (2, ln 2) into the equation to find the specific value of dy/dx at that point.