Question

$\huge\boxed{\dfrac{\partial }{\partial \:x}\left(\sqrt{x^2+y^2}\right)}$

Question for real life genius

Answer 1

Explanation:

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Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\bf{\dfrac{\partial }{\partial \:x}\left(\sqrt{x^2+y^2}\right)}$

♣ ᴀɴꜱᴡᴇʀ :

$\bf{Treat\:y\: as \:a \:constant}$

$\bf{Apply\: the\: chain\: rule: \dfrac{1}{2 \sqrt{x^{2}+y^{2}}} \dfrac{\partial}{\partial x}\left(x^{2}+y^{2}\right)}}$

$\bf{=\dfrac{1}{2 \sqrt{x^{2}+y^{2}}} \dfrac{\partial}{\partial x}\left(x^{2}+y^{2}\right)}$

$\bf{\dfrac{\partial}{\partial x}\left(x^{2}+y^{2}\right)=2 x}$

$\bf{=\dfrac{1}{2 \sqrt{x^{2}+y^{2}}} \cdot 2 x}$

$\bf{Simplify\:\frac{1}{2 \sqrt{x^{2}+y^{2}}} \cdot 2 x: \dfrac{x}{\sqrt{x^{2}+y^{2}}}}$

$\boxed{=\dfrac{\mathbf{X}}{\sqrt{\mathbf{x}^{2}+\mathbf{y}^{2}}}}$