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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (2 x^{2} + 2 y^{2}) = 4 x + 4 y \frac{d y}{d x}

= \frac{1}{2 2 x ^{2} + 2 y ^{2}} (4 x + 4 y \frac{d y}{d x})

簡素化

\frac{1}{2 2 x ^{2} + 2 y ^{2}} (4 x + 4 y \frac{d y}{d x}) : \frac{2 ( x + y \frac{d y}{d x} )}{2 x ^{2} + 2 y ^{2}}

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