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I was using This Wolfram Alpha Page to calculate the partial derivatives of the sum of two gaussians. It believes the answer to be: $ e^{-(b-x)^2/2 c^2} $ but the working shows it as ending on: $ e^{-(x-b)^2/2 c^2} $ Which is what I had thought the answer was.

Is this a bug in Wolfram's engine or have I missed an obvious step?

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It:$(x-b)^{2} = (b-x)^{2} \ \ \forall b,x \in \mathbb{R}$

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    Of course, complete brain-fart over here. Thanks2011-12-06
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have I missed an obvious step?

Yes