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

Lösung

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

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

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Wende die Produktregel an:

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

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

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

\frac{\partial}{\partial x} (x + z) = 1

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

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

Vereinfache

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

\int \frac{1}{( 6 x - 1 ) ^{2}} d x

\frac{d}{d x} (- 16 x^{2})

\frac{\partial}{\partial z} (9 z e^{x yz})

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

\frac{\partial}{\partial x} (\frac{1}{5 x ^{4}})