What is the derivative of f(x)=cos(-x)-cos(x)?

1 Answer
Nov 3, 2015

It's just a tricky way to write the identitcal-zero function, so the derivative is zero.

Explanation:

I'd say that no derivatives are needed, since you know that cos(-x)=cos(x), and so

cos(-x)=cos(x) = cos(x)-cos(x) = 0, and the derivative of 0 is of course 0.

Anyway, even if we didn't notice that, we can do the derivatives: since the derivative of cos(x) is -sin(x), we have (using the chain rule for the first term)

-sin(-x) * (d/dx (-x)) - (-sin(x))

and since (d/dx (-x))=-1, the expression becomes

sin(-x) +sin(x)

Again, you should use the fact that sin(-x)=-sin(x), and so the sum is again zero.