Need an example of piece wise function continuous but not differentiable

Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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