derivative of arctan(x+2y)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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