Answer
(a)$f(x)=4(e^{1.5x})(1.5^x)$
(b)$f^{'}(x)=(4 \ln 1.5)(e^{1.5x})(1.5^x)+6(1.5^x)e^{1.5x} $
Work Step by Step
$g(x)=2e^{1.5x}$
$h(x)=2 (1.5^x)$
(a)
Let
$f(x)=g(x)h(x)$
$f(x)=2e^{1.5x}\times2(1.5^x)=4(e^{1.5x})(1.5^x)$
(b)Taking derivative of f(x) with respect to x
$f^{'}(x)=4(e^{1.5x})\frac{d(1.5^x)}{dx}+4(1.5^x)\frac{d(e^{1.5x})}{dx}$
$f^{'}(x)=4(e^{1.5x})(1.5^x)(\ln 1.5)+4(1.5^x)e^{1.5x} \frac{d(1.5x)}{dx}$
$f^{'}(x)=4(e^{1.5x})(1.5^x)(\ln 1.5)+4(1.5^x)e^{1.5x} (1.5)\frac{d(x)}{dx}$
$f^{'}(x)=4(e^{1.5x})(1.5^x)(\ln 1.5)+4(1.5^x)e^{1.5x} (1.5)$
$f^{'}(x)=(4 \ln 1.5)(e^{1.5x})(1.5^x)+4(1.5)(1.5^x)e^{1.5x} $
$f^{'}(x)=(4 \ln 1.5)(e^{1.5x})(1.5^x)+6(1.5^x)e^{1.5x} $
