$19\mathrm{.}2$ Find $f(1),$ the derivative at $x=1,$ of the following functions.

$($a$)f(x)=3x^{10}+2x^5+x+e^x$

$($b$)f(x)=\frac{x^2-2x+5}{1+x}$

$($c$)f(x)=\frac{1}{1-\sqrt[\phantom{2}]{x}+x^2}$

$($d$)f(x)=(x^2+4x+6{)}^5$