Answer
$(0.3x^{1.1}-4x^{-3.1})\cdot(7x-1)+ x^{2.1}+14x^{-2.1}$
Work Step by Step
$f(x)= \displaystyle \frac{1}{7}x^{2.1}+2x^{-2.1}, \ \ \quad g(x)=7x-1,\quad y=f(x)\cdot g(x)$
$f^{\prime}(x)=\displaystyle \frac{1}{7}(2.1x^{1.1}+2(-2.1x^{-3.1})=0.3x^{1.1}-4x^{-3.1}$
$g^{\prime}(x)=7$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[f(x)\cdot g(x)]$= ... product rule ...
=$f^{\prime}(x)g(x)+f(x)g^{\prime}(x)$
$=(0.3x^{1.1}-4x^{-3.1})\displaystyle \cdot(7x-1)+( \frac{1}{7}x^{2.1}+2x^{-2.1})\cdot 7$
$=(0.3x^{1.1}-4x^{-3.1})\cdot(7x-1)+ x^{2.1}+14x^{-2.1}$
... we do not need to expand the answer..