Question

How to take the derivative of e^(xy)=cy with respect to x?

Answer 1

First, what is derivative of e^x?

Answer 2

So e^(xy)=e^(x)*e^(y) and to take the derivative with respect to x, it's e^(xy), right? What about the RHS?

Answer 3

No.
e^(xy) = (e^x)^y, not e^x * e^y
e^x * e*y = e^(x + y)

Answer 4

The right side is simply cy, so its derivative is cy'

Answer 5

We need to work on the left side.

Answer 6

If \(y = e^u\), for u, a function of x, then
\(y' = e^u u'\)

Answer 7

So how to differentiate (e^x)^y?