Remember that if n is a positive integer then
The same holds for all the other trig functions as well of course. Also remember to keep the following straight.
In the first case we taking the tangent then squaring result and in the second we are squaring the x then taking the tangent.
The tan x^2 is actually not the best notation for this type of problem. We really should probably use tan( x^2) to make things clear.
Another thing to always keep in mind is that -1 in the cos^-1(x) is NOT an exponent , it is there to denote the fact that we are dealing with an inverse trig function. ie.
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