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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

y^{^{'}} = 5 y^{2}

d er i v a t i v e y = 25 - x - 9 x^{2}

\frac{d}{d x} ((x^{2} - 5)^{3})

x \to - 3 lim (+ (f (x)))

ma c l a u r in e^{θ}