@Nukchebi0:
What is the derivative of x^(1/3) and -x(1/3)? I tried finding an equation that eliminated 0 from the denominator, but failed. I also tried using the “cheat” method (x^n ->
nx^(x-1), but couldn’t see how this was implemented.
If possible could you show the algebra steps? I don’t need the calculus notation, but would like to know how it works, not just the answer.
You said that you tried to eliminate the 0 from the denominator.
I answered that it is a problem of discontinuity. Deriving a function you are worsening the function properties. Example: x^(1/3) is continuous and defined in all the set of real number R. Its derivated function (1/3) * x^(-2/3) is discontinuous in the point 0, where it is not defined.
If you need to do some operation that uses those two derivative in the point 0, you may not use them, becasue for x = 0 the two functions are not defined, their value simply does not exist.