Help With Partial Derivative

Question

$$ A=(A_0/z)\exp[-jk(x^{2}+y^{2})/2z] $$ $$ \frac{\partial{A}}{\partial{x}} = -jxA\frac{k}{z} $$ Can anybody explain why this is the case? I thought that exponential functions never disappeared when one does derivatives.

Answer 1

Well, it doesn't disappear. What you didn't write is, that A is a function depending on $x$. Actually you have

$\partial_x A = -jk\frac{k}{z}A(x)$

and the $\exp$ is included in your function A(x). This is the prototype of an ordinary differential equation.

Answer 2

Let $B=e^x$. Then $B'=B$. Has the exponential dísappeared?

Answer 3

It didn't disappear. Note that the $-jx\frac k z$ came from the chain rule, and the rest was left alone, hiding in the $A$.