What is the derivative of $sqrtx^2$ ?

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Answer 1 · 2015-06-22T14:13:10

The root of a square is the number itself.

$sqrtx^2=x$

The derivative of this is $1$

Answer 2 · 2015-06-22T14:39:15

If $f(x) = sqrtx^2$ , the $f(x) = x$ , so $f'(x) = 1$ , but

Be careful:

$g(x)=sqrt(x^2) = abs(x) = {(x, "if",x >= 0),(-x,"if",x<0) :}$

So $g'(x) = {(1, "if",x > 0),(-1,"if",x<0) :}$

$g'(0)$ does not exist.

What is the derivative of sqrtx^2sqrtx^2?