(\partial)/(\partial x)(x^6y^8+7x^7y)

Lösung

\frac{\partial}{\partial x} (x^{6} y^{8} + 7 x^{7} y)

6 y^{8} x^{5} + 49 y x^{6}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{6} y^{8} + 7 x^{7} y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{6} y^{8}) + \frac{\partial}{\partial x} (7 x^{7} y)

\frac{\partial}{\partial x} (x^{6} y^{8}) = 6 y^{8} x^{5}

\frac{\partial}{\partial x} (7 x^{7} y) = 49 y x^{6}

= 6 y^{8} x^{5} + 49 y x^{6}

\int x^{2} sin (x^{3} + 4) d x

a re a y = 4 - x^{2}, y = - 3 x

\int_{1}^{2} π (\frac{1}{x})^{2} d x

\int_{5}^{11} \frac{16}{x - 1} d x

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