Let's start by converting this to the from #f(x) = (g(x))/(h(x))#.
#f(x) = ((3 - 5x)/(5x))/(2/(x^2 + 7))#
#f(x) = ((3 - 5x)(x^2 + 7))/(10x)#
#f(x) = (3x^2 - 5x^3 - 35x + 21)/(10x)#
The derivative of a function #f(x) = (g(x))/(h(x))# is given by #color(red)(f'(x) = (g'(x) * h(x) - h'(x)g(x))/(h(x))^2#
#f'(x) = ((-15x^2 + 6x - 35)(10x) - 10(3x^2- 5x^3 - 35x + 21))/(10x)^2#
#f'(x) = (-150x^3 + 60x^2 - 350x - 30x^2 + 50x^3 + 350x -210)/(100x^2)#
#f'(x) = (-100x^3 + 30x^2 - 210)/(100x^2)#
#f'(x) = (-10(10x^3 - 3x^2 + 21))/(100x^2)#
#f'(x) = -(10x^3 - 3x^2 + 21)/(10x^2)#
Hopefully this helps!
