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

Lösung

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

9 x^{2} + 8 x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (3 x^{3}) = 9 x^{2}

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

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

= 9 x^{2} + 8 y x - 0

Vereinfache

= 9 x^{2} + 8 x y

in v erse l a pl a ce \frac{3 s + 7}{s ^{2} - 2 s - 3}

\frac{d}{d x} (ln (x e^{x} + 7))

\int_{0}^{2} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

\frac{d}{d y} (\frac{y ^{3}}{21} + \frac{7}{4 y})

d er i v a t i v e f (x) = 8 x + ln (x^{2})