Which one of the following is correct regarding stability factor with standard notations?

Stability factor (S):

It is the rate of change of collector current (IC) with respect to the reverse saturation current of collector junction (ICO), i.e.

\(S = \frac{{\partial {I_C}}}{{\partial {I_{CO}}}}\)       ---(1)

We know that collector current is given by:

IC = β IB + (1 + β) ICO     ---(2)

Differentiating equation (2) w.r.t IC and treating β as constant, we can write:

\(1 = \beta \times \frac{{\partial {I_B}}}{{\partial {I_C}}} + \left( {1 + \beta } \right)\frac{{\partial {I_{CO}}}}{{\partial {I_C}}}\)

\(\frac{{\partial {I_{CO}}}}{{\partial {I_C}}} = \frac{{1 - \beta \frac{{\partial {I_B}}}{{\partial {I_C}}}}}{{1 + \beta }}\)

\(\frac{{\partial {I_C}}}{{\partial {I_{CO}}}} = \frac{{1 + \beta }}{{1 - \beta \frac{{\partial {I_B}}}{{\partial {I_C}}}}}\)    ---(3)

From (1) & (3), we get:

Stability factor (S) will be:

\(S = \frac{{\partial {I_C}}}{{\partial {I_{CO}}}} = \frac{{1 + \beta }}{{1 - \beta \frac{{\partial {I_B}}}{{\partial {I_C}}}}}\)