(\partial)/(\partial x)(sin(y^2)+6e^x)

解

\frac{\partial}{\partial x} (sin (y^{2}) + 6 e^{x})

6 e^{x}

解答ステップ

\frac{\partial}{\partial x} (sin (y^{2}) + 6 e^{x})

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 (y^{2})) + \frac{\partial}{\partial x} (6 e^{x})

\frac{\partial}{\partial x} (sin (y^{2})) = 0

\frac{\partial}{\partial x} (6 e^{x}) = 6 e^{x}

= 0 + 6 e^{x}

簡素化

= 6 e^{x}