(\partial)/(\partial x)(2x*sin(9x^2y))

解

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

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

解答ステップ

\frac{\partial}{\partial x} (2 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^{'}

= 2 \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)

= 2 (\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

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

簡素化

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

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