(\partial)/(\partial x)(6x^7y^4+2x^6y^8)

Lösung

\frac{\partial}{\partial x} (6 x^{7} y^{4} + 2 x^{6} y^{8})

42 y^{4} x^{6} + 12 y^{8} x^{5}

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x^{7} y^{4} + 2 x^{6} y^{8})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (6 x^{7} y^{4}) + \frac{\partial}{\partial x} (2 x^{6} y^{8})

\frac{\partial}{\partial x} (6 x^{7} y^{4}) = 42 y^{4} x^{6}

\frac{\partial}{\partial x} (2 x^{6} y^{8}) = 12 y^{8} x^{5}

= 42 y^{4} x^{6} + 12 y^{8} x^{5}

s l o p e 4 y^{3} + 7 x^{8} = 5 y + 6 x, (1, 1)

n = 1 \sum \infty (\frac{5}{2})^{n}

\frac{d}{d x} (\frac{( x ^{3} + 8 )}{2 x})^{7}

d er i v a t i v e u^{6}

x \to 0 lim ((\frac{1}{x})^{x})