d/(d{x)}(({z})(-e^{{z}}+{x}^2+{y}^2+{z}^2))

解

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

2 z x

解答ステップ

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

定数を除去:

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

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (e^{z}) = 0

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

\frac{d}{d x} (y^{2}) = 0

\frac{d}{d x} (z^{2}) = 0

= z (- 0 + 2 x + 0 + 0)

簡素化

= 2 z x