Recall that the derivative of a function f at a point x is denoted as f'(x).
The given function: `f(x)= arcsin(x)+arccos(x)` has inverse trigonometric terms.
There are basic formulas for the derivative of inverse trigonometric functions:
`d/(dx) (arcsin(u)) = ((du)/(dx))/sqrt(1-u^2)`
`d/(dx) (arccos(u)) = -((du)/(dx))/sqrt(1-u^2). `
Applying the formula in the given function:
`f'(x) =d/(dx) (arcsin(x)) +d/(dx) (arccos(x))`
`f'(x) =1/sqrt(1-x^2) + (-1/sqrt(1-x^2))`
`f'(x) =1/sqrt(1-x^2) -1/sqrt(1-x^2)`
`f'(x) =0`
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