derivative of ,xe^y+y^2x-x^3,\at (1,0)

解

\frac{d}{d x} (, x e^{y} + y^{2} x - x^{3}, at (1, 0))

(, (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x)) + 2 x y \frac{d y}{d x} + y^{2} - (, at (1, 0) \cdot 3 x^{3 - 1})

解答ステップ

\frac{d}{d x} (, x e^{y} + y^{2} x - x^{3}, at (1, 0))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (, x e^{y}) + \frac{d}{d x} (y^{2} x) - \frac{d}{d x} (x^{3}, at (1, 0))

\frac{d}{d x} (, x e^{y}) = (, (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x))

\frac{d}{d x} (y^{2} x) = 2 x y \frac{d y}{d x} + y^{2}

\frac{d}{d x} (x^{3}, at (1, 0)) = (, at (1, 0) \cdot 3 x^{3 - 1})

= (, (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x)) + 2 x y \frac{d y}{d x} + y^{2} - (, at (1, 0) \cdot 3 x^{3 - 1})