Finding Derivative of sinx: What do I do Next?

[iRaid]

I know the derivative is cosx but I don't know what to do.
So I get the derivative of sinx down to:
$$\frac{sinxcosh}{h} - \frac{sinx}{h} + \frac{cosxsinh}{h}$$

What do I do after that?
(not a homework problem)

 

[micromass]

Hi iRaid!

First about notation: don't forget the limit!

I see that you need to calculate two limits now:

$$\lim_{h\rightarrow 0}{\frac{\cos(h)-1}{h}}=0~~\text{and}~~\lim_{h\rightarrow 0}{\frac{\sin(h)}{h}}=1$$

The second limit should be known to you (if not, see http://www.khanacademy.org/video/proof--lim--sin-x--x?playlist=Calculus for a nice derivation).
The first limit follows from the second by multiplying numerator and denominator by 1+cos(x).

 

[rock.freak667]

You should simplify sinxcosh+coshsinx into one simple trig function and then use the http://www.sosmath.com/trig/prodform/prodform.html" .

 

[iRaid]

You should simplify sinxcosh+coshsinx into one simple trig function and then use the http://www.sosmath.com/trig/prodform/prodform.html" .

Well that makes it much easier also @micromass, thanks too :) and I didn't forget the limit, just I didn't know how to do it in latex :p