Given: $f(x)=10x\sqrt[\phantom{2}]{3x^2+2x+10}$; find $f^{\text{'}}(x).$

$f^{\text{'}}(x)=\sqrt[\phantom{2}]{3x^2+2x+10}+\frac{3x^2}{\sqrt[\phantom{2}]{3x^2+2x+10}}$

$f^{\text{'}}(x)=10\sqrt[\phantom{2}]{3x^2+2x+10}+\frac{10x}{\sqrt[\phantom{2}]{3x^2+2x+10}}$

$f^{\text{'}}(x)=\frac{30x^2}{\sqrt[\phantom{2}]{3x^2+2x+10}}$

$f^{\text{'}}(x)=10\sqrt[\phantom{2}]{3x^2+2x+10}+\frac{15x^2}{\sqrt[\phantom{2}]{3x^2+2x+10}}$

$f^{\text{'}}(x)=10\sqrt[\phantom{2}]{3x^2+2x+10}+\frac{10x(3x+1)}{\sqrt[\phantom{2}]{3x^2+2x+10}}$

None of the above.