(\partial)/(\partial x)(9xsin(4x^2y))

解

\frac{\partial}{\partial x} (9 x sin (4 x^{2} y))

9 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

解答ステップ

\frac{\partial}{\partial x} (9 x sin (4 x^{2} y))

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} (x sin (4 x^{2} y))

積の法則を適用:

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

f = x, g = sin (4 x^{2} y)

= 9 (\frac{\partial}{\partial x} (x) sin (4 x^{2} y) + \frac{\partial}{\partial x} (sin (4 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (4 x^{2} y)) = cos (4 x^{2} y) \cdot 8 y x

= 9 (1 \cdot sin (4 x^{2} y) + cos (4 x^{2} y) \cdot 8 y xx)

簡素化

9 (1 \cdot sin (4 x^{2} y) + cos (4 x^{2} y) \cdot 8 y xx) : 9 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

= 9 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))