Answer
$\frac{5}{2}$
Work Step by Step
$(fog)'$ = $f'(g(x))g'(x)$
$(fog)'(1)$ = $f'(g(1))g'(1)$
$g(x)$ = $\sqrt x$
$g(1)$ = $\sqrt 1$ = $1$
$g'(x)$ = $\frac{1}{2\sqrt x}$
$g'(1)$ = $\frac{1}{2\sqrt 1}$ = $\frac{1}{2}$
$f(u)$ = $u^{5}+1$
$f'(u)$ = $5u^{4}$
$u$ = $g(x)$ = $\sqrt x$
$f'(u)$ = $f'(g(x))$ = $5(\sqrt x)^{4}$ = $5x^{2}$
$f'(g(1))$ = $5(^1){2}$ = $5$
$(fog)'(1)$ = $f'(g(1))g'(1)$ = $(5)$$(\frac{1}{2})$ = $\frac{5}{2}$
