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

解

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

ln (y) z

解答ステップ

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

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{d}{d x} (y z) = 0

\frac{d}{d x} (x ln (y)) = ln (y)

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

= z (0 + ln (y) - 0)

簡素化

= ln (y) z