(\partial)/(\partial y)(sin(x)+x^2e^y-1)

解

\frac{\partial}{\partial y} (sin (x) + x^{2} e^{y} - 1)

e^{y} x^{2}

解答ステップ

\frac{\partial}{\partial y} (sin (x) + x^{2} e^{y} - 1)

x

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} (sin (x)) + \frac{\partial}{\partial y} (x^{2} e^{y}) - \frac{\partial}{\partial y} (1)

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

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

\frac{\partial}{\partial y} (1) = 0

= 0 + x^{2} e^{y} - 0

簡素化

= e^{y} x^{2}