(\partial)/(\partial y)(x^2+3xy+y-1)

Lösung

\frac{\partial}{\partial y} (x^{2} + 3 x y + y - 1)

3 x + 1

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} + 3 x y + y - 1)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (3 x y) + \frac{\partial}{\partial y} (y) - \frac{\partial}{\partial y} (1)

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

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

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (1) = 0

= 0 + 3 x + 1 - 0

Vereinfache

= 3 x + 1

d er i v a t i v e (6 x - 2)^{2}

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

\int 8 sin (8 x) d x

t an g e n t y = x^{2} e^{x} - 2 x e^{x} + 2 e^{x}

d er i v a t i v e f (x) = \frac{24 x}{2 x + 3}