Answer
$g^{'}(4e^w)= 10e^w(7+20e^w)^{-0.5} $
Work Step by Step
$g(x)=\sqrt {7+5x} ; x(w)=4e^w$
Composite function will be:
$g(4e^w)=\sqrt { 7+5(4)e^w} $
$g(4e^w)=\sqrt { 7+20e^w} $
$g(4e^w)= (7+20e^w)^{0.5} $
Taking derivative with respect to w
$g^{'}(4e^w)= (0.5)(7+20e^w)^{0.5-1} \frac{d(7+20e^w)}{dw} $
$g^{'}(4e^w)= (0.5)(7+20e^w)^{-0.5} 20e^w $
$g^{'}(4e^w)= (0.5)20e^w(7+20e^w)^{-0.5} $
$g^{'}(4e^w)= 10e^w(7+20e^w)^{-0.5} $
