Find the derivative for each function, leave no negative exponents. no square root in denominator and simplify your answer fully.

a$)f(x)=\frac{x^3-5}{x+6}$

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

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

d$)f(x)=\frac{x^{\frac{2}{3}}-7}{x+9}$