(\partial)/(\partial x)(x^3-y^3+6xy)

Lösung

\frac{\partial}{\partial x} (x^{3} - y^{3} + 6 x y)

3 x^{2} + 6 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} - y^{3} + 6 x 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} (y^{3}) + \frac{\partial}{\partial x} (6 x y)

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

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

\frac{\partial}{\partial x} (6 x y) = 6 y

= 3 x^{2} - 0 + 6 y

Vereinfache

= 3 x^{2} + 6 y

\int 1 + e^{x} d x

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

t an g e n t f (x) = x^{2} + 3 x + 1, (- 1, - 1)

\int \frac{2}{( x + 1 ) ^{3}} d x

\frac{d}{d y} (x^{2} y^{2})