Is a power function necessarily differentiable in its domain of definition?

Is a power function necessarily differentiable in its domain of definition?

not always
For example, y = x ^ (1 / 3), the domain is r
But at x = 0, it is not differentiable

Find the domain of the following power functions
（1）y=x^(2/3)
（2）y=x^（5/6）
（3）y=x^（-4/5）
（4）y=x^（-3/2）
The trouble is the process

（1）y=x^(2/3) x=R
（2）y=x^（5/6）
x>=0
（3）y=x^（-4/5）
Unequal zero
（4）y=x^（-3/2）
x=R+

Graph of exponential function
How to draw the image of y = 2 ^ x ^ 2-x?
It's best to draw or describe it!

The problem is often too complicated to start with. The actual point is OK. It's better to list and draw more points. The image will probably be drawn. However, it's important to draw the image when x > 0 first, and then draw X

What is the fixed point of exponential function image

(0,1) image is like "skim" or "Na"