derivative of x*sin(y)

解

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

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

解答ステップ

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

積の法則を適用:

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

f = x, g = sin (y)

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

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

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

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

簡素化

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