Find the derivative of the function.

Answer

cos(arccos *x*) = *x*,

taking derivatives of both sides,

-sin (arccos *x*)(arccos *x*)' = 1

which means

If we let θ = arccos *x*, then somewhere there's a right triangle with an angle θ such that

That triangle looks something like this:

Using the Pythagorean theorem, the missing side of the triangle is

therefore

Then