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MathCalculus

Differentiation of x^(1/2): Find the Derivative of √x

For positive x, differentiating √x gives 1/(2√x). The function is real-valued at zero, but its right-hand difference quotient has no finite limit there.

Question

Calculate the derivative of

f(x)=x=x1/2.f(x)=\sqrt{x}=x^{1/2}.

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Evidence boundary

The keyword is interpreted as x1/2=sqrtxx^{1/2}=sqrt{x} over the real numbers. The derivative formula 1/(2sqrtx)1/(2sqrt{x}) applies for x>0x>0; it is not a finite derivative at x=0x=0.