Derivative help of y=cosx!

1. Oct 14, 2007

lilxchristina

how do you find the derivative of y=cosx by using the limit process of

limit as h --> 0 is f(x+h) - f(x) / all over h.

i did this with y=sinx, and the answer was cosx, but i'm having trouble figuring out y=cosx.

help?

2. Oct 14, 2007

arildno

Well,
$$\frac{\cos(x+h)-cos(x)}{h}=\frac{\cos(h)-1}{h}\cos(x)-\frac{\sin(h)}{h}\sin(x)=-\frac{\sin(h)}{h}(\frac{\sin(h)}{\cos(h)+1}\cos(x)+\sin(x))$$
using well-known identities. Can you finish this?

Last edited: Oct 14, 2007
3. Oct 14, 2007

ZioX

You need to know that

$$\lim_{t\to 0} \frac{\sin(t)}{t}=1.$$

The most common elementary proof of this is geometric.