# D/dx sinc(x)

1. Jan 21, 2010

### mherna48

Hey can anyone help me prove that the derivative of sin(x)/x is zero at x=0

2. Jan 22, 2010

### snipez90

A function f:R -> R is differentiable at 0 if
$$\lim_{h \rightarrow 0}\frac{f(h)-f(0)}{h}$$
exists. You can apply this definition and then use l'Hopital's rule or perhaps some first-order estimates to show that this last limit exists. Alternatively, you can probably work directly with the series expansion for sin.

3. Jan 22, 2010

### evagelos

`
But f(0) = sin0/0 is not defined

4. Jan 22, 2010

### snipez90

Well I took it that the OP actually meant the sinc function, which just extends f(x) = sin(x)/x by continuity so that f(0) = 1.