Need an example of piece wise function continuous but not differentiable

I Need an example of piece wise function continuous but not differentiable. One of the functions has to be trigonometric and the other has to be exponential. Please

Hint: Let $f(x)=\cos x$ for $x\le 0$ and let $f(x)=e^x$ for $x\gt 0$.

$$f(x)=\left\{\begin{array}{ll}\cos(x)& x\leq 0\\e^x &x>0\end{array}\right.$$

$$\sin(|x|)$$ $$\mathrm{e}^{-|x|}$$

You may consider the function$$f(x)=\sin x$$ for $x<0$ and $$f(x)=e^{2x}-1$$ for $x>0$

• "the functions has to be trigonometric and the other has to be exponential" – Dario Jun 17 '14 at 6:31
• @Dario- Yes, edited accordingly – freebird Jun 17 '14 at 6:32
• This new one is not continuous (moreover it is not defined in 0). – Dario Jun 17 '14 at 6:32
• @Dario- I don't know what is wrong with me today. I suppose it should be OK now. – freebird Jun 17 '14 at 6:36
• Now it's fine :) – Dario Jun 17 '14 at 6:37