(\partial)/(\partial x)(sqrt(x^2+y^2)+1)

解

\frac{\partial}{\partial x} (x^{2} + y^{2} + 1)

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

解答ステップ

\frac{\partial}{\partial x} (x^{2} + y^{2} + 1)

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} (x^{2} + y^{2}) + \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (1) = 0

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

簡素化

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