Question

Calculus Fan and Medal!
If e^(xy) = 4, then what is dy/dx at the point (1, ln4)?

Answer 1

this is tricky

let u = xy

by chain rule

du /dx = d e^u * du
---- --
dx dx

Answer 2

* thats d e^u / du

Answer 3

e ^xy * d (xy) = d (4)/dx
dx

Answer 4

Okay so I basically solve for the implicit derivative of that equality? From there how do I bring in the points given?

Answer 5

just plug in x = 1 and y = ln 4

Answer 6

d(xy)/dx = y + x dy/dx ( product rule)