# Help With Partial Derivative

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

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It didn't disappear it is still in the $A$ at the right! –  Raymond Manzoni Oct 14 '12 at 21:44
Do not loose track that it is an implicit derivative. The derived function actually appears in its derived expression. –  busman Oct 14 '12 at 21:47
I see now. Thanks everyone. –  John Roberts Oct 14 '12 at 21:51

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