If you know that the derivative of sine of x with respect to x is cosine of x, and the derivative of cosine of x with respect to x is negative sine of x, that can empower you to do many more, far more complicated derivatives. But what we're gonna do in this video is dig a little bit deeper and actually prove this first derivative. I'm not gonna prove the second one. You can actually use it using the information we're going to do in this one. But it's just to make you feel good that someone's just not making this up, that there is a little bit of mathematical rigor behind it all. So let's try to calculate it. So the derivative with respect to x of sine of x.