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

Lösung

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

2 x + 2 y

Schritte zur Lösung

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

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

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

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

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

= 0 + 2 y + 2 x

Vereinfache

= 2 x + 2 y

in v erse l a pl a ce \frac{( 6 s + 3 )}{s ^{4} + 5 s ^{2} + 4}

d er i v a t i v e - sin (x) - \frac{1}{2}

d er i v a t i v e 4 x + 1

\int \frac{1}{8 - 4 sin ( x ) + 7 cos ( x )} d x

\int - x ln (x) d x