Answer:
a. [tex]\frac{2(x-6)(x-2)}{(x^2+4)^2}[/tex]
Step-by-step explanation:
a. f'(x) = [tex]\frac{x(3x-2)}{x^2+4}[/tex]
b. f'(x) = [tex]\frac{2(x^2-6x-1)}{(x-3)^2}[/tex]
using quotient rule and product rule
f'(x) = [tex]\frac{[(3x-2)+3x](x^2+4)-(2x)[x(3x-2)]}{(x^2+4)^2}[/tex]
f'(x) = [tex]\frac{(6x-2)(x^2+4)-2x(3x^2-2x)}{(x^2+4)^2}[/tex]
f'(x) = [tex]\frac{(6x^3-2x^2+24x-8)-(6x^3-4x^2)}{(x^2+4)^2}[/tex]
f'(x) = [tex]\frac{2x^2+24x-8}{(x^2+4)^2}[/tex] = [tex]\frac{2(x-6)(x-2)}{(x^2+4)^2}[/tex]
b. f'(x) = [tex]\frac{[(2x-1)+2(x+1)](x-3)-(x+1)(2x-1)}{(x-3)^2}[/tex]
f'(x) = [tex]\frac{(4x+1)(x-3)-(x+1)(2x-1)}{(x-3)^2}[/tex]
f'(x) = [tex]\frac{(4x^2-11x-3)-(2x^2+x-1)}{(x-3)^2}[/tex]
f'(x) = [tex]\frac{2x^2-12x-2}{(x-3)^2}[/tex]
f'(x) = [tex]\frac{2(x^2-6x-1)}{(x-3)^2}[/tex]
