(\partial)/(\partial y)(e^{xz}y^3-ln(x))

解

\frac{\partial}{\partial y} (e^{x z} y^{3} - ln (x))

3 e^{x z} y^{2}

解答ステップ

\frac{\partial}{\partial y} (e^{x z} y^{3} - ln (x))

x, z

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial y} (e^{x z} y^{3}) - \frac{\partial}{\partial y} (ln (x))

\frac{\partial}{\partial y} (e^{x z} y^{3}) = 3 e^{x z} y^{2}

\frac{\partial}{\partial y} (ln (x)) = 0

= 3 e^{x z} y^{2} - 0

簡素化

= 3 e^{x z} y^{2}