Answer
(a)$f(x)=0.5(0.8^x).(6-14\ln x)$
(b)$f^{'}(x)= 0.5(0.8^x)\ln 0.8(6-14 \ln x)+0.5(0.8^x)[-14(\frac{1}{x})]$
Work Step by Step
$g(x)=0.5(0.8^x);h(x)=6-14\ln x$
(a)
Let $f(x)=g(x)h(x)$
$f(x)=0.5(0.8^x).(6-14\ln x)$
(b)
Taking derivative of f(x) with respect to x
$f^{'}(x)= g^{'}(x)h(x)+g(x)h^{'}(x)$
$f^{'}(x)= 0.5(0.8^x)\ln 0.8(6-14 \ln x)+0.5(0.8^x)[0-14(\frac{1}{x})]$
$f^{'}(x)= 0.5(0.8^x)\ln 0.8(6-14 \ln x)+0.5(0.8^x)[-14(\frac{1}{x})]$
