Answer
(a)$f(x)=(3x^{-0.7}).(5^x)$
(b)$f^{'}(x)=-2.1x^{-1.7}] (5^x)+(3x^{-0.7}) 5^x \ln 5$
Work Step by Step
$g(x)=3x^{-0.7};h(x)=5^x$
(a)
Let $f(x)=g(x)h(x)$
$f(x)=(3x^{-0.7}).(5^x)$
(b)
Taking derivatives of f(x) with respect to x, using product rule
$f^{'}(x)=g^{'}(x)h(x)+g(x)h^{'}(x)$
$f^{'}(x)=3(-0.7)x^{-0.7-1} (5^x)+(3x^{-0.7}) 5^x \ln 5$
$f^{'}(x)=-2.1x^{-0.7-1} (5^x)+(3x^{-0.7}) 5^x \ln 5$
$f^{'}(x)=-2.1x^{-1.7} (5^x)+(3x^{-0.7}) 5^x \ln 5$
