<p>Well, the statement you made earlier was a proof using the instantaneous rate of change definition.</p>
<p>Of course, there are other “proofs” that work well as well.</p>
<p>For instance, a basic knowledge of the relationship between f and f ’ will also suggest the relationship between the derivative of y = sin x and y = cos x.</p>
<p>I don’t mean to imply that it’s unimportant to take a look at why things work the way they do.</p>
<p>But I also think there are too many people who think they should also re-derive everything on the test, which is just as poor an idea.</p>