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

Lösung

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

4 x y^{3}

Schritte zur Lösung

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

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^{4})

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

\frac{\partial}{\partial y} (x y^{4}) = 4 x y^{3}

= 0 + 4 x y^{3}

Vereinfache

= 4 x y^{3}

\int_{1}^{x} \frac{1}{t} d t

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

d er i v a t i v e y = \frac{x - x}{x ^{2}}

\frac{d}{d t} (5 t + 4 t^{5})

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