(\partial)/(\partial x)(xsin^2(x))

解

\frac{\partial}{\partial x} (x sin^{2} (x))

sin^{2} (x) + x sin (2 x)

解答ステップ

\frac{\partial}{\partial x} (x sin^{2} (x))

積の法則を適用:

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

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

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

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

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

= 1 \cdot sin^{2} (x) + sin (2 x) x

簡素化

= sin^{2} (x) + x sin (2 x)