(\partial)/(\partial x)(5xsin(3x^2y))

解

\frac{\partial}{\partial x} (5 x sin (3 x^{2} y))

5 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

解答ステップ

\frac{\partial}{\partial x} (5 x sin (3 x^{2} y))

y

を定数として扱う

定数を除去:

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

= 5 \frac{\partial}{\partial x} (x sin (3 x^{2} y))

積の法則を適用:

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

f = x, g = sin (3 x^{2} y)

= 5 (\frac{\partial}{\partial x} (x) sin (3 x^{2} y) + \frac{\partial}{\partial x} (sin (3 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (3 x^{2} y)) = cos (3 x^{2} y) \cdot 6 y x

= 5 (1 \cdot sin (3 x^{2} y) + cos (3 x^{2} y) \cdot 6 y xx)

簡素化

5 (1 \cdot sin (3 x^{2} y) + cos (3 x^{2} y) \cdot 6 y xx) : 5 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))

= 5 (sin (3 x^{2} y) + 6 x^{2} y cos (3 x^{2} y))