(\partial)/(\partial x)((x+y^2)e^{x-y})

Lösung

\frac{\partial}{\partial x} ((x + y^{2}) e^{x - y})

e^{x - y} + e^{x - y} (x + y^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + y^{2}) e^{x - y})

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x + y^{2}, g = e^{x - y}

= \frac{\partial}{\partial x} (x + y^{2}) e^{x - y} + \frac{\partial}{\partial x} (e^{x - y}) (x + y^{2})

\frac{\partial}{\partial x} (x + y^{2}) = 1

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

= 1 \cdot e^{x - y} + e^{x - y} (x + y^{2})

Vereinfache

= e^{x - y} + e^{x - y} (x + y^{2})

\int_{- 6}^{1} - 2 x^{2} - 10 x + 12 d x

\int ((x - 1)^{2} - (x + 1)^{2}) (x^{3} + 1) d x

\frac{\partial}{\partial x} (z ln (y) + e^{2})

\frac{d}{d x} (3 9 x^{2} + 4)

\frac{d}{d x} (x^{2} arcsinh (9 x))