Practise power, chain and product rules together

For $x>0$, the expression is $2x^{-1/2}+6x^{-1/3}$. Differentiate to get $-x^{-3/2}-2x^{-4/3}$, matching the printed answer. The square-root denominator restricts the combined real domain to $x>0$.

The derivative is $8x(x^2+3)^3(2x^3-5)^3+18x^2(x^2+3)^4(2x^3-5)^2$.

Take out $2x(x^2+3)^3(2x^3-5)^2$. The remaining bracket is $4(2x^3-5)+9x(x^2+3)=17x^3+27x-20$. Thus the result is $2x(x^2+3)^3(2x^3-5)^2(17x^3+27x-20)$, exactly the printed answer. This polynomial derivative is valid for all real $x$; factoring does not exclude zeros of the factors.