Answer
(a)$f(x)=(5x^2-3)(1.2^x)$
(b)$f^{'}(x)= 1.2^x(10x)+(5x^2-3)(1.2^x ) \ln 1.2$
Work Step by Step
$g(x)=(5x^2-3); h(x)=1.2^x$
(a)Let
$f(x)=g(x)h(x)$
$\Longrightarrow$
$f(x)=(5x^2-3)(1.2^x)$
(b)
Taking derivative of f(x) with respect to x, using product rule
$f^{'}(x)= 1.2^x\frac{d(5x^2-3)}{dx}+(5x^2-3)\frac{d(1.2^x)}{dx}$
Using the formula
$\frac{d(a^x)}{dx}=a^x\ln a$
$f^{'}(x)= 1.2^x(10x)+(5x^2-3)(1.2^x ) \ln 1.2$
