$In$ Exercises $1-30,$ find the derivative $of$ each function.

$f(x)=2x(x^2+1)$

$f(x)=3x^2(x-1)$

$f(t)=(t-1)(2t+1)$

$f(x)=(2x+3)(3x-4)$

$f(x)=(3x+1)(x^2-2)$

$f(x)=(x+1)(2x^2-3x+1)$

$f(x)=(x^3-1)(x+1)$

$f(x)=(x^3-12x)(3x^2+2x)$

$f(w)=(w^3-w^2+w-1)(w^2+2)$

$f(x)=\frac{1}{5}{x}^5+(x^2+1)(x^2-x-1)+28$

$f(x)=(5x^2+1)(2\sqrt[\phantom{2}]{x}-1)$

$f(t)=(1+\sqrt[\phantom{2}]{t})(2t^2-3)$

$f(x)=(x^2-5x+2)(x-\frac{2}{x})$

$f(x)=(x^3+2x+1)(2+\frac{1}{x^2})$

$f(x)=\frac{1}{x-2}$

$g(x)=\frac{3}{2x+4}+2x^2$