Solving Mechanics Question: Show Energy of Motion in x-z Plane

[Varnson]

Homework Statement

A particle slides under gravity along a smooth path in the x-z plane by z=b-(x^2/a).
Show that the energy of this motion can be expressed as E=.5m*xdot^2*[1+(2x/a)^2] + mgb[1-(x^2/ab)]

Homework Equations

T(A)+V(A) = T(B)+V(B), where T is kinetic energy

The Attempt at a Solution

I understand how to get the potential energy term, but I am confused on how to calculate the kinetic term.

 

[azatkgz]

$$v^2=\dot z^2+\dot x^2$$

$$\dot z=-\frac{2x\dot x}{a}$$