(\partial)/(\partial x)(z-sqrt(x^2+y^2))

解

\frac{\partial}{\partial x} (z - x^{2} + y^{2})

- \frac{x}{x ^{2} + y ^{2}}

解答ステップ

\frac{\partial}{\partial x} (z - x^{2} + y^{2})

z, y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (z) - \frac{\partial}{\partial x} (x^{2} + y^{2})

\frac{\partial}{\partial x} (z) = 0

\frac{\partial}{\partial x} (x^{2} + y^{2}) = \frac{x}{x ^{2} + y ^{2}}

= 0 - \frac{x}{x ^{2} + y ^{2}}

簡素化

= - \frac{x}{x ^{2} + y ^{2}}