Math problem with physics derivation.

Relativistic energy is sometimes derived in the following manner and I'm having trouble deciphering one mathematical step. It uses integration by substitution. So it goes like this: Given that
F=\frac{dp}{dt}
and reletavistic momentum is given by p=\frac{ mv }{ sqrt(1-\frac{v^2}{c^2}) } W=int_{x _{1}}^{x_{2}} F dx=int_{x _{1}}^{x_{2}} \frac{dp}{dt}dx which is fine then they say \frac{dp}{dt}=\frac{d}{dt}\frac{mv}{sqrt(1-(\frac{v^2}{c^2}))}=\frac{m(dv/dt)}{(1-(\frac{v^2}{c^2}))^\frac{3}{2}} its that last step that i dont understand. why does the denominator term now have a 3/2 index? and why is du/dt given in such an odd way?

Question

Math problem with physics derivation.

Relativistic energy is sometimes derived in the following manner and I'm having trouble deciphering one mathematical step. It uses integration by substitution. So it goes like this: Given that
F=\frac{dp}{dt}
and reletavistic momentum is given by p=\frac{ mv }{ sqrt(1-\frac{v^2}{c^2}) } W=int_{x _{1}}^{x_{2}} F dx=int_{x _{1}}^{x_{2}} \frac{dp}{dt}dx which is fine then they say \frac{dp}{dt}=\frac{d}{dt}\frac{mv}{sqrt(1-(\frac{v^2}{c^2}))}=\frac{m(dv/dt)}{(1-(\frac{v^2}{c^2}))^\frac{3}{2}} its that last step that i dont understand. why does the denominator term now have a 3/2 index? and why is du/dt given in such an odd way?