d/(dy)(1/2 ln(x^2+y^2))

解

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

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

解答ステップ

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

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d y} (ln (x^{2} + y^{2}))

連鎖法則を適用:

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

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

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

= \frac{1}{2} \cdot \frac{1}{x ^{2} + y ^{2}} \cdot 2 y

簡素化

\frac{1}{2} \cdot \frac{1}{x ^{2} + y ^{2}} \cdot 2 y : \frac{y}{x ^{2} + y ^{2}}

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