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Thermal stability coefficient

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The thermal stability coefficient is defined to be:

$S = \frac{dI_{C}}{dI_{CBO}}$ where $I_{CBO}$ is the reverse current of the BJT when voltage isnt applied to the base of the BJT.

In case of a BJT biased with 2 sources $I_{C} = \beta \cdot I_{b}+(\beta +1)I_{CBO}$

However my textbook says that $S = \frac{1+\beta}{1-\beta\frac{dI_{b}}{dI_{C}}}$

however I dont get why that is the case.Any help?

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If "base voltage isn't applied" then Ib=0 & dIb=0 then the proposed formula with Ib is not logical.

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