(\partial)/(\partial y)(x^2-xy+4y^2)

Lösung

\frac{\partial}{\partial y} (x^{2} - x y + 4 y^{2})

8 y - x

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} - x y + 4 y^{2})

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} (x y) + \frac{\partial}{\partial y} (4 y^{2})

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

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

\frac{\partial}{\partial y} (4 y^{2}) = 8 y

= 0 - x + 8 y

Vereinfache

= 8 y - x

x \to 2 lim (2 x - 7)

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

\frac{d}{d x} (4^{c o s (x)})

\int \frac{x ^{3}}{( x ^{2} + 1 ) ^{2}} d x

x \to - 5 lim (\frac{x - 5}{x + 5})