High School Derivative of Square Root of x at 0

[mopit_011]

When you use the power rule to differentiate the square root, the result is 1/2(sqrt. x) which is undefined at 0. But, when you use the definition of the definition of the derivative to calculate it, the result is infinity. What causes this difference between these two methods?

 

[PeroK]

Infinity is undefined in this context.

 

[fresh_42]

When you use the power rule to differentiate the square root, the result is 1/2(sqrt. x) which is undefined at 0. But, when you use the definition of the definition of the derivative to calculate it, the result is infinity. What causes this difference between these two methods?

None. The derivative of $x\longmapsto \sqrt{x}$ isn't defined for $x=0$ in neither case.

 

[Office_Shredder]

Some might also observe that
$$\lim_{x\to 0^+} \frac{1}{2\sqrt{x}}$$
Is also infinity.