Example of function so that is continuous but its derivative is not.

mathKing

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Hello, I try to find a example of function f so that is continuous on [0,1] x [0,1], but its derivative is not.
I've spent all day trying to find it, please help me.
 
Hello, I try to find a example of function f so that is continuous on [0,1] x [0,1], but its derivative is not.
I've spent all day trying to find it, please help me.

Have you considered Rational Functions or Piecewise definitions?
 
Hello, I try to find a example of function f so that is continuous on [0,1] x [0,1], but its derivative is not.
I've spent all day trying to find it, please help me.

Consider piecewise function definition. f(x) = g(x) on [0,0.5], f(x) = h(x) on (0.5,1]. g(x) and h(x) should have the same value at 0.5, but different derivatives.
What's [0,1] x [0,1]? Are we looking at 2 variable functions?
 
Thank you, I will try find piecewise function. I don't exactly know whether is should be 2 variables, I got such a notation from my professor, have a look at this 20181121-121635.jpg
 

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Hello, I try to find a example of function f so that is continuous on [0,1] x [0,1], but its derivative is not.
I've spent all day trying to find it, please help me.
I'd play with the absolute value function.
 
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