Question

What is $f^{\text{'}}(x)$ when $f(x)=(5x^2+3{)}^{\frac{1}{2}}?$

Select the correct answer below:

$f^{\text{'}}(x)=(5x^2+3{)}^{\frac{1}{2}}(\frac{-1}{x^2}ln(5x^2+3)+\frac{1}{x(5x^2+3)})$

$f^{\text{'}}(x)=\frac{-1}{x^2}(ln(5x^2+3))(5x^2+3{)}^{\frac{1}{2}}$

$f^{\text{'}}(x)=(\frac{1}{x})(5x^2+3{)}^{\frac{1}{2}}-1$

$f^{\text{'}}(x)=(5x^2+3{)}^{\frac{1}{2}}(\frac{-1}{x^2}ln(5x^2+3)+\frac{10}{5x^2+3})$