find the derivative:

Question

d/dx int_a to x (a being the upper limit) of tan(tan(t))dt

Answer 1

Graph a function(any function) from a to x.
I think you mean a is the lower limit and x the upper, but whatever:

The question is what is the change of area under that function for a small change in the upper limit x of dx?
It is in fact the value of the function at x times dx
and d/dx of that is just the value of the function at x
tan [tan(x)]