derivative of xsin(x^3)

解

\frac{d}{d x} (x sin (x^{3}))

sin (x^{3}) + 3 x^{3} cos (x^{3})

解答ステップ

\frac{d}{d x} (x sin (x^{3}))

積の法則を適用:

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

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

= \frac{d x}{d x} sin (x^{3}) + \frac{d}{d x} (sin (x^{3})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

= 1 \cdot sin (x^{3}) + cos (x^{3}) \cdot 3 x^{2} x

簡素化

1 \cdot sin (x^{3}) + cos (x^{3}) \cdot 3 x^{2} x : sin (x^{3}) + 3 x^{3} cos (x^{3})

= sin (x^{3}) + 3 x^{3} cos (x^{3})