Hi,

I am being given the following question:

Let f(x) = tan(sin x2)−sin(tan x2). Let n be the smallest positive integer
such that f(^(n))(0) 6= 0. Then n = __.

I am suppose to differentiate f(x) using maple to solve for n, that is to differentiate the function over and over again till I am able to get say f(^(16))=0.

However, maple gets very laggy after i tried n=10.

Is there any shortcut that could help solve this problem?

Best regards,

zn.