Got it!!!

(a) (vz)/(c^2sqrt(1-v^2/c^2)^3)

I made it m=z(1-v^2/c^2)^(-1/2)

then to find the derivative i used the chain rule

(-1/2)z(1-v^2/c^2)^(-3/2)((2v(c^2))/(c^4))

bring the (1-v^2/c^2)^(-3/2) to the denominator and it simplifies to: (vz)/(c^2sqrt(1-v^2/c^2)^3)

That really doesnt look like it makes sense because it is so hard to read but i get it

(b) the rate of change of mass with respect to the speed