derivative of 3(x^2+y^2^2)

解

\frac{d}{d x} (3 (x^{2} + y^{2})^{2})

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

解答ステップ

\frac{d}{d x} (3 (x^{2} + y^{2})^{2})

定数を除去:

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

= 3 \frac{d}{d x} ((x^{2} + y^{2})^{2})

連鎖法則を適用:

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

= 2 (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}

= 3 \cdot 2 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x})

簡素化

= 6 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x})