(\partial)/(\partial x)(xe^y-e^z)

Lösung

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

e^{y}

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (e^{z}) = 0

= e^{y} - 0

Vereinfache

= e^{y}

im pl i c i t \frac{d y}{d x}, y e^{x} = y

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

\int \frac{sin ( 2 x )}{sin ( x )} d x

\frac{\partial}{\partial x} (\frac{1 - ln ( x )}{x ^{2}})

\frac{\partial}{\partial x} (ln (9 x))