Answer: [tex]\bold{-7-14x-x^{-\frac{2}{3}}}[/tex]
Step-by-step explanation:
[tex]x^{\frac{1}{3}}[-7x^{\frac{2}{3}}-(7x^{\frac{5}{3}}+3)]\\\\\\\underline{\text{Distribute }x^{\frac{1}{3}}}\\-7x-7x^2-3x^{\frac{1}{3}}\\\\\\\underline{\text{Now find the derivative of each term:}}\\g(x)= 7x\implies g'(x)=7\\h(x) = -7x^2\implies h'(x)=-14x\\j(x)=-3x^{\frac{1}{3}}\implies j'(x)=-x^{-\frac{2}{3}}\\\\\underline{\text{Now combine the terms:}}\\f'(x) =g'(x)+h'(x)+j'(x)\quad =\large\boxed{7-14x-x^{-\frac{2}{3}}}[/tex]
