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So I got into wolfram to see whether I solved correctly an exercise.

More specifically the first-order derivative of $y(x)=e^x (ax^4+bx^3+cx^2+dx+q)$.

Im solving by undetermined coefficients the particular solution of $y'''+3y''-6y'+6y=2x^4e^x$

This is what Wolfram returned

Why is the first term multiplying $e^x$ with a $log(e)$, I mean, why isnt ${\dfrac{d e^x}{dx}} = e^x?$

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    If you need $e^x$ type $Exp[x]$ – 2017-01-15
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    Damn man that was fast. Thanks and sorry for the dumb question. – 2017-01-15
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    Wasn't dumb, now you know more about Wolfram Alpha. – 2017-01-15
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    Also Wolfram Alpha recognizes Euler's constant by capital E. – 2017-01-15

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Looks like a case of Wolfram Alpha being too smart for its own good. The input you entered was:

derivative e^x * (ax^4+bx^3+cx^2+dx+q)

Note that the expression uses the constants $a,b,c,d\,$. Apparently, this trips WA into assuming that $e$ must itself be such an arbitrary constant. If you change the expression to use, say, $p$ instead of $d$ then WA will assume that $e$ is the base of the natural logarithms, instead:

derivative e^x * (ax^4+bx^3+cx^2+px+q)

The workarounds have already been posted in comments: use $Exp(x)\,$, or use the capital $E^x\,$.