Differentiation in Mathematica

Question

I want to differentiate f(x)=sin(x^2-1) in Mathematica Software

I used this command

D[Sin[x^2 - 1], x]

The output is

2 x Cos[1 - x^2]

Why the angle is 1-x^2 instead of x^2-1 ??

Thanks.

Answer 1

Because the cosine function is even, the two forms are equivalent (cos(x^2 - 1) = cos(1 - x^2)).

Apparently the simplification algorithms Mathematica uses were a tad over-enthusiastic in this case.