Why is it that $\frac{d}{dx}((a+2bx)e^{3x}) \neq \frac{d}{dx}((ae^{3x}+2bxe^{3x}))$

Question

I was computing a differential equation and I ended up with the following result: $\frac{d}{dx}((a+2bx)e^{3x})$. My intuition was to distribute $e^{3x}$, however I got the wrong answer.

When I wrote down both equations into Wolfram Alpha, I got different results.

Why is that the case? Why can't I distribute?

Wolfram alpha:

• Distributing
• Not Distributing

Answer 1

Notice some of the notation Wolfram Alpha is using in the first case:

It is putting $a'$ and $a''$ and such, even though you presumably meant it as a constant.

That is, Wolfram Alpha is seemingly interpreting $a$ as a function, with argument $e^{3x}$.

Indeed, editing your input to include an asterisk, to more explicitly indicate multiplication, seems to fix this.

Answer 2

The first is wrong, Wolfram detect a as a function of x, and used partial differentiation, I recommend using symbolab instead of wolfram.