Well the number e, raised to 6 (e^6) is just a number (a constant), so you integrate a constant times dx gives you that constant times x + C --> x*e^6 + C
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The first derivative of e to the x power is e to the power of x.
The anti-derivative of 1/x is ln|x| + C, where ln refers to logarithm of x to the base e and |x| refers to the absolute value of x, and C is a constant.
The derivative of xe is e. The derivative of xe is exe-1.
e is not derivative. Please reconsider your question, clarify what you wish to ask and resubmit.
The derivative of ex is ex