Carefully work out each problem, show all your intermediate steps and clearly indicate your final answer.

Problem $1.(10$ points$)$ Compute the derivative of each function.

$($a$)$

$f(x)=\frac{1}{\sqrt[\phantom{2}]{3x^2+5x-1}}$

$($b$)$

$g(x)=(-3x+6)(5x+1{)}^{\frac{3}{2}}$