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

Lösung

\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})

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(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})

\int x^{2} arcsin (x) d x

\frac{d}{d x} (- \frac{2}{5 x})

\frac{d}{d x} (\frac{x + 2}{ln ( x )})

\frac{\partial}{\partial y} (e^{\frac{y}{x}} - \frac{e ^{\frac{y}{x}} y}{x})

\int_{0}^{1} x 1 - x d x