There is a function which is continuous but not differentiable I have a function which is a convergent series:
$$f(x) = \sin(x) + \frac{1}{10}\sin(10x) + \frac{1}{100}\sin(100x) + \cdots \frac{1}{10^n}\sin(10^nx)$$
This function is convergent because for any E you care to specify, the function has a term which is smaller than E.  However, the function is not differentiable, and I don't understand why.
$$\frac{d}{dx}f(x) = \cos(x)+\frac{10}{10}\cos(10x) + \frac{100}{100}\cos(100x) + \cdots \frac{10^n}{10^n}\cos(10^nx)$$
Is this a special case to A Continuous Nowhere-Differentiable Function ?

Notice that if you plug $x=k\pi$, where $k$ is any integer, into the derivative of the that function, you get $\infty$, thereby making the derivative discontinuous. This, in other words, means that the function is not differentiable.
