(\partial)/(\partial x)(x^2+y^2+3xy+5x)

Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 5 x)

2 x + 3 y + 5

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 5 x)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (3 x y) = 3 y

\frac{\partial}{\partial x} (5 x) = 5

= 2 x + 0 + 3 y + 5

Vereinfache

= 2 x + 3 y + 5

x^{2} y^{^{'}} + (2 - y) = 0

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

\frac{\partial}{\partial x} (7 x y^{3} + 5)

t^{2} y^{^{'}} + 2 t y - y^{3} = 0

d er i v a t i v e ln ∣ t ∣