That's actually a fairly involved proof that proves this. But if we assume this, I'm gonna make a visual argument that this right over here is true, that the derivative with respect to x of cosine of x is negative sine of x. So right over here, we see sine of x in red and we see cosine of x in blue. And we're assuming that this blue graph is showing the derivative, the slope of the tangent line for any x value of the red graph. And we've gotten an intuition for that in previous videos. Now what I'm gonna do next is I'm gonna shift both of these graphs to the left by pi over two. Shift it to the left by pi over two.