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

解

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

y^{2} (2 x cos (x) - x^{2} sin (x))

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = cos (x)

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

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

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

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

簡素化

= y^{2} (2 x cos (x) - x^{2} sin (x))