Question: confused about a differentiation

I am having a problem differentiating a function. I have a fluid in a channel with moving walls corresponding to y=a(t) (upper wall) and y=-a(t) (lower wall). The fluid is driven by suction out of the walls. The speed of the fluid being sucked out of the walls is the constant v_w. I am using the variable eta=y/a(t) to model the fluid. y is the normal direction to teh channel and x is the streamwise direction of the channel. So I have

x=streamwise direction of the channel

y=normal direction of the channel

a(t)=height of the channel



eta=y/a(t) is the similarity variable

u=streamwise velocity


I want top partially differentiate Xi with respect to t.

I am confused as a(t) depends on t, eta depends on a(t) which in turn depends on t and F depends on t. What would i write on maple to get the correct differentiation?


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