(\partial)/(\partial y)(x^2-xy^2+4y^5)

Lösung

\frac{\partial}{\partial y} (x^{2} - x y^{2} + 4 y^{5})

20 y^{4} - 2 x y

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} - x y^{2} + 4 y^{5})

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^{2}) + \frac{\partial}{\partial y} (4 y^{5})

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

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

\frac{\partial}{\partial y} (4 y^{5}) = 20 y^{4}

= 0 - 2 x y + 20 y^{4}

Vereinfache

= 20 y^{4} - 2 x y

\frac{\partial}{\partial y} (sin (x) cos (y))

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

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

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

in v erse l a pl a ce \frac{1}{( s - 1 ) ^{2} + 1}