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

Lösung

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

3 x^{2} - 2 y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

\frac{\partial}{\partial x} (y^{3}) = 0

= 3 x^{2} - 2 y^{2} - 0

Vereinfache

= 3 x^{2} - 2 y^{2}

\int_{0}^{0.5} (200 x) d x

s im pl i f y \frac{1}{u}

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

\int (9 x^{8} + 10 x^{5} - 5 x^{2} - 5) d x

\int e^{- 3 x} + ln (3) - \frac{1}{x} d x