derivative of (x+ye^y)

Lösung

\frac{d}{d x} ((x + y) e^{y})

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

Schritte zur Lösung

\frac{d}{d x} ((x + y) e^{y})

Wende die Produktregel an:

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

f = x + y, g = e^{y}

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

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

\frac{d}{d x} (e^{y}) = e^{y} \frac{d y}{d x}

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

x \to - \frac{1}{2} lim (4 x (3 x + 4)^{2})

a \to t lim (a^{5} + a^{5})

\frac{\partial}{\partial z} (x y^{2} arctan (z))

\int_{1}^{2} \frac{3}{x ^{2}} d x

\frac{\partial}{\partial x} (x x y)