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

解

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

4 (sin (9 x^{2} y) + 18 x^{2} y cos (9 x^{2} y))

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

積の法則を適用:

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

f = x, g = sin (9 x^{2} y)

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

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

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

= 4 (1 \cdot sin (9 x^{2} y) + cos (9 x^{2} y) \cdot 18 y xx)

簡素化

4 (1 \cdot sin (9 x^{2} y) + cos (9 x^{2} y) \cdot 18 y xx) : 4 (sin (9 x^{2} y) + 18 x^{2} y cos (9 x^{2} y))

= 4 (sin (9 x^{2} y) + 18 x^{2} y cos (9 x^{2} y))