how can we define eletrochemistry and what is eltrolysis in simple words and derive the expression of nernst equation

@ surendra 
electrochemistry is actually a branch of chemistry that deals of electrical and chemical phenomena , that means to convert electrical energy into chemical energy . (to use electricity for doing chemical reaction ) and also vice versa ., 
ELECTROLYSIS , is a method of using a direct current (DC ) to drive an otherwise non spontaneous chemical reaction .
for example when electricity is being passed through water , then it decomposes to o2 and h2 . 
that u have to understand only .. 

and in the case of nernest equation , there are no derivation for that .
THEY HAVE JUST 2-3 FORMS THAT U HAVE TO LEARN AND IN QUESTION U HAVE TO SEE WHICH FORM WILL BE APPLICABLE WHERE . 
I AM GIVING THE MOST STANDARD FORM OF NERNEST EQUATION 
Enot (CELL ) = E(CELL ) – 0.0591 / N LOG [cathode]/ [anode]
and in the above equation N represent the no of electron being participated in the chemical reaction . 
HOPE IT CLEARS YOUR DOUBT 
IF MORE ASK IT . PLZZ APOPROVE MY ANSWER . 
ALL THE BEST ..