(\partial)/(\partial x)(9cos(xy)x)

解

\frac{\partial}{\partial x} (9 cos (x y) x)

9 (- x y sin (x y) + cos (x y))

解答ステップ

\frac{\partial}{\partial x} (9 cos (x y) x)

y

を定数として扱う

定数を除去:

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

= 9 \frac{\partial}{\partial x} (cos (x y) x)

積の法則を適用:

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

f = cos (x y), g = x

= 9 (\frac{\partial}{\partial x} (cos (x y)) x + \frac{\partial}{\partial x} (x) cos (x y))

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

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

= 9 ((- sin (x y) y) x + 1 \cdot cos (x y))

簡素化

= 9 (- x y sin (x y) + cos (x y))