(\partial)/(\partial x)(8x^5y^6+6x^4y^8)

Lösung

\frac{\partial}{\partial x} (8 x^{5} y^{6} + 6 x^{4} y^{8})

40 y^{6} x^{4} + 24 y^{8} x^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (8 x^{5} y^{6} + 6 x^{4} y^{8})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (8 x^{5} y^{6}) + \frac{\partial}{\partial x} (6 x^{4} y^{8})

\frac{\partial}{\partial x} (8 x^{5} y^{6}) = 40 y^{6} x^{4}

\frac{\partial}{\partial x} (6 x^{4} y^{8}) = 24 y^{8} x^{3}

= 40 y^{6} x^{4} + 24 y^{8} x^{3}

d er i v a t i v e 6 x^{- 4}

\frac{\partial}{\partial x} (5 y^{\frac{1}{4}} x^{\frac{1}{2}})

\int x^{3} 4 + x^{4} d x

\int (3 4 x^{3} - 8 x^{5} + 6 e^{x} - 2) d x

\frac{d y}{d x} = y (3 - y)