(\partial)/(\partial x)(x^3+x^2y-y^2-4y)

Lösung

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

3 x^{2} + 2 x y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

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

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

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

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

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

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

Vereinfache

= 3 x^{2} + 2 x y

\frac{d}{d x} (4 x + 5)

x \to 5 + lim (\frac{2}{x + 5})

\frac{\partial}{\partial x} (a x + b y^{2} + c x^{2} y)

\frac{d}{d x} (arctan (tan (x)))

x \to 0 + lim (x ln (x^{2}))