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

解

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

2 e^{y} x + cos (x)

解答ステップ

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

y

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

\frac{\partial}{\partial x} (sin (x)) = cos (x)

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

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

= cos (x) + 2 e^{y} x - 0

簡素化

= 2 e^{y} x + cos (x)