(\partial)/(\partial x)(x^4-x^3y+xy^3-y^4)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{\partial}{\partial x} (y^{4}) = 0

= 4 x^{3} - 3 y x^{2} + y^{3} - 0

Vereinfache

= 4 x^{3} - 3 x^{2} y + y^{3}

x \to 0 lim (\frac{1}{x} + \frac{1}{∣ x ∣})

d er i v a t i v e y = \frac{x ^{6}}{6} + \frac{1}{16 x ^{4}}

\int_{- 1}^{1} \frac{x ^{2}}{1 + x ^{6}} d x

d er i v a t i v e \frac{cos ( x )}{e ^{x}}

\int (7 x^{2} - 4 x) e^{2 x} d x