Floor Function And Derivatives: The Case Of [Sin X]

What is the derivative [sin x]

Cos x

The derivative of [sin x], where [ ] represents the floor function or greatest integer function, is not defined for integer values of x. This is because the floor function changes abruptly at integer values, causing a discontinuity in the derivative.

However, for non-integer values of x, we can take the derivative of sin x and then round down to the nearest integer. This gives us:

[d/dx [sin x]] = cos x

Therefore, for non-integer values of x, the derivative of [sin x] is equal to the floor of cos x.

More Answers:

[next_post_link]