(\partial)/(\partial x)(x*Y(x))

解

\frac{\partial}{\partial x} (x \cdot Y (x))

Y (x) + x \frac{\partial}{\partial x} (Y (x))

解答ステップ

\frac{\partial}{\partial x} (x Y (x))

積の法則を適用:

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

f = x, g = Y (x)

= \frac{\partial}{\partial x} (x) Y (x) + \frac{\partial}{\partial x} (Y (x)) x

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

= 1 \cdot Y (x) + \frac{\partial}{\partial x} (Y (x)) x

簡素化

= Y (x) + x \frac{\partial}{\partial x} (Y (x))