Question

Find all values of x for which the function is Differentiable at P(x) = sin (| x |) -1

Answer 1

i doubt that

Answer 2

if \(x<0\) then \(\sin(|x|)=\sin(-x)\) and so the derivative would be \(-\cos(x)\)

Answer 3

\[D_x \sin(x)=\cos(x)\\
\begin{cases}|x|=x, \;\;x\geq0 \\
|x|=-x, \;\;x<0
\end{cases}\\
\cos(-x)=cos(x)\\
\sin(-x)=-\sin(x)
\]
If x < 0 Dx[sin(|x|)]=Dx[sin(-x)]=-cos(x)

Answer 4

and since at 0 \(-\cos(0)\neq \cos(0)\) it is not differentiable there

Answer 5

it is not continuity it is differentiability