THE FIRST ORDER REACTION THAT PROCEED AT A RATE THAT DEPENDS LINEARLY ON ONLY ONE REACTANT CONCENTRATION.
We know from the rate law that,R=-d[R]/dt=K[A]1=K[A]
                                                  d[A]/[A]=-Kdt
 Integrating both side,                [Ao]/[A]=-[to]/[t]Kdt
  Recall from calculus that,           1/X=ln[x]
                                                     ln[A]-ln[Ao]=-kt
                                                     ln[A]=ln[Ao]-Kt
                                                      ln[A]=-Kt+ln[Ao]
 This can be further arranged intoY=mx+c,  ln[A]=kt+ln[Ao]
   This equation is a straight line with slope m,               mx=-kt
                                                                            b = ln[Ao]
    from the LAW OF LOGARITHM,                     ln{[A]t/[Ao]} = -kt  
 [A]is the concentration at time T,[Ao] is the concentration at time 0.K is the rate constant.
 
Charecterestic of first order reation are.
The concentration of [A] decreases exponentially with time.The decrese is such that the time required for a definite fraction of the reaction to occur is independent of the initial concentration of the reaction.
The rate of the reaction directly proportional to the conc. of the reactant.
The rate of the reaction is directly proportional to the square root of the conc. of the reactant.                                                                                                                                                                                     
						

							
@ hitesh 
the full derivation is well expplained in ncert , and just read it once , and let me know if u are facing any problem in any perticular steps , i will explain only that step briefly , rather that will be good , i think . 
and remember the formula for the rate constant . 
k = 2.303/ t log {R0] / [R]
AND always u can interchange the position of k and t as well . 
and the half life for frst order reaction is 
t (1/2 ) = 0.693 / k 
CHARECTERISTICS 
1- it will obey the first order kinetics , 
2- the sum total of the the power raised to the concentration term in rate equation will must equal to 1 when add up
3- THE RATE OF THE REACTION DOESNOT depend upon the initial conc. of reactant .. 
HOPE IT HELPS