Well, another problem here I don't get.
From what I know, sin(x)'=cos(x) right?
Well, here is a problem:
Find $\frac{d}{dx}(y\cos(\frac{y}{x^4}))$ ?
Let $u=y\cos(\frac{y}{x^4})$ and $s=y$, $v=\cos(\frac{y}{x^4})$
u'=v\frac{ds}{dx}+s \frac{dv}{dx}
u'=\cos\frac{y}{x^4} \frac{dy}{dx} + y \frac{d}{dx}(\cos\frac{y}{x^4})
Now the question, isn't $\frac{d}{dx}(\cos\frac{y}{x^4})=-\sin(\frac{y}{x^4})$ and here it's where it all ends? Why is the teacher going on and differentiates what's in the parentheses?