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

Lösung

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

3 x^{2} - y

Schritte zur Lösung

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

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

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

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

= 3 x^{2} - y + 0

Vereinfache

= 3 x^{2} - y

x \to 1 lim (x^{\frac{7}{1 - x}})

\frac{d}{d x} (3 4 x)

\int \frac{4 x}{( x ^{2} + 1 )} d x

\int 5 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

t an g e n t f (x) = \frac{11}{9 x}, at x = 1