derivative of xsin(xy)

解

\frac{d}{d x} (x sin (x y))

sin (x y) + x cos (x y) (y + x \frac{d y}{d x})

解答ステップ

\frac{d}{d x} (x sin (x y))

積の法則を適用:

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

f = x, g = sin (x y)

= \frac{d x}{d x} sin (x y) + \frac{d}{d x} (sin (x y)) x

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

\frac{d}{d x} (sin (x y)) = cos (x y) (y + x \frac{d y}{d x})

= 1 \cdot sin (x y) + cos (x y) (y + x \frac{d y}{d x}) x

簡素化

= sin (x y) + x cos (x y) (y + x \frac{d y}{d x})