d/(d{y)}(({x})(ln(cos({x}+{y}))+e^{{x}}{y}{z}))

解

\frac{d}{d y} ((x) (ln (cos (x + y)) + e^{x} y z))

x - \frac{sin ( x + y ) ( \frac{d}{d y} ( x ) + 1 )}{cos ( x + y )} + e^{x} z

解答ステップ

\frac{d}{d y} ((x) (ln (cos (x + y)) + e^{x} y z))

定数を除去:

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

= x \frac{d}{d y} (ln (cos (x + y)) + e^{x} y z)

和/差の法則を適用:

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

= x (\frac{d}{d y} (ln (cos (x + y))) + \frac{d}{d y} (e^{x} y z))

\frac{d}{d y} (ln (cos (x + y))) = - \frac{sin ( x + y ) ( \frac{d}{d y} ( x ) + 1 )}{cos ( x + y )}

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

= x - \frac{sin ( x + y ) ( \frac{d}{d y} ( x ) + 1 )}{cos ( x + y )} + e^{x} z