Capacitor output differentiation issue
In this case 'e' is not a variable it is a constant: eulers number, ~2.718.... more commonly known as the base of natural log, ln().  

The derivation rules for an exponential function such as a^x (where a is constant) state that the derivative for:
$$\frac{d}{dx}a^x = a^x \ln(a)$$

In your case, we have another constant to worry about, the 2 in front of the x. In which case, we copy down the constant to in front of the base (not bring it down as you were thinking) so:
$$\frac{d}{dx}a^{bx} = b a^{bx} \ln(a)$$
Where b is another constant.

So, there is one more point remaining, \$\ln(e) = 1\$. Relplacing \$a\$ with \$e\$ means that:
$$be^{bx}\ln(e) = b e^{bx}$$
by simply replacing b with 2, we get what wolfram alfa told you for the derivative of \$e^{2x}\$.

The main point: What you were thinking about differentiation is when the variable is the base of the exponent, not when the variable is in the exponent itself.