Prove that the square root of (x^2 + y^2) is not differentiable at the point (0,0,0).
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Step 1: Start with the given function \( f(x, y) = \sqrt{x^2 + y^2} \). Show more…
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Key Concepts
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Show that if $f$ is differentiable at $x$ and $f(x) > 0,$ then $$\frac{d}{d x} \sqrt{f(x)}=\frac{f^{\prime}(x)}{2 \sqrt{f(x)}}$$ Use this Square Root Rule to find the derivative of $\sqrt{x^{2}+1}.$
Differentiation
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