Answer
$1$
Work Step by Step
$(fog)'(x)$ = $f'(g(x))g'(x)$
$g(x)$ = $\frac{1}{1-x}$
$g(-1)$ = $\frac{1}{1+1}$ = $\frac{1}{2}$
$g'(x)$ = $\frac{1}{(1-x)^{2}}$
$g'(-1)$ = $\frac{1}{(1+1)^{2}}$ = $\frac{1}{4}$
$f(u)$ = $1-\frac{1}{u}$
$f'(u)$ = $\frac{1}{u^{2}}$
$f'(u)$ = $f'(g(x))$ = $\frac{1}{(\frac{1}{1-x})^{2}}$ = $(1-x)^{2}$
$f'(g(-1))$ = $(1+1)^{2}$ = $4$
$(fog)'(-1)$ = $f'(g(-1))g'(-1)$ = $(4)$$(\frac{1}{4})$ = $1$
