(\partial)/(\partial x)(-9x^2y^2-cos(y))

解

\frac{\partial}{\partial x} (- 9 x^{2} y^{2} - cos (y))

- 18 x y^{2}

解答ステップ

\frac{\partial}{\partial x} (- 9 x^{2} y^{2} - cos (y))

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} (9 x^{2} y^{2}) - \frac{\partial}{\partial x} (cos (y))

\frac{\partial}{\partial x} (9 x^{2} y^{2}) = 18 y^{2} x

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

= - 18 y^{2} x - 0

簡素化

= - 18 x y^{2}