(\partial)/(\partial y)((z)(e^{xz}+xy))

Lösung

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

z x

Schritte zur Lösung

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

Behandle

z, x

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= z (0 + x)

Vereinfache

= z x

e x p an d a (- 2, - \frac{π}{3})

e x p an d \frac{10 x ^{2} + 7 x - 42}{( x - 2 ) ( x + 4 ) ( x - 1 )}

\frac{d}{d x} ((z) (sin (y z) - x - 2 y - 3 z))

e x p an d t^{2} e^{t} u (t - 1)

e x p an d lo g_{10} (7) (a^{2} b^{3} c)