Answer
(a)$f(x)=g(x)h(x)=(6 \ln 3x).[7(5^x)+8]$
(b)$f^{'}(x)= \frac{6}{x} [7(5^x)+8]+(6\ln 3x)[7(5^x)\ln 5]$
Work Step by Step
$g(x)=6\ln 3x; h(x)=7(5^x)+8$
(a)
Let $f(x)=g(x)h(x)$
$f(x)=g(x)h(x)=(6 \ln 3x).[7(5^x)+8]$
(b)
$f^{'}(x)=g^{'}(x)h(x)+g(x)h^{'}(x)$
$f^{'}(x)= 6\frac{1}{3x} (3)[7(5^x)+8]+(6\ln 3x)[7(5^x)\ln 5]$
$f^{'}(x)= \frac{6}{x} [7(5^x)+8]+(6\ln 3x)[7(5^x)\ln 5]$
