derivative of 2ln(x^2+y^2)

解

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

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

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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