# Talk:Moment Generating Function of Geometric Distribution/Formulation 1/Examples/First Moment

 $\ds \map { {M_X}'} t$ $=$ $\ds \map {\frac \d {\d t} } {\dfrac {1 - p} {1 - p e^t} }$ Moment Generating Function of Geometric Distribution $\ds$ $=$ $\ds \dfrac {-\paren {1 - p} \paren {-p e^t } } {\paren {1 - p e^t}^2 }$ Quotient Rule for Derivatives, Derivative of Exponential Function $\ds$ $=$ $\ds \dfrac {\paren {1 - p} \paren {p e^t} } {\paren {1 - p e^t}^2 }$ get rid of all that confusing negativeness $\ds$ $=$ $\ds \dfrac {p e^t - p^2 e^t} {\paren {1 - p e^t}^2}$
which is not the same as $\dfrac {p e^t } {\paren {1 - p e^t} }$
No wait - it's ok - $\paren {1 - p e^t}$ cancels