(\partial)/(\partial x)(x^7y^8+3x^5y)

Lösung

\frac{\partial}{\partial x} (x^{7} y^{8} + 3 x^{5} y)

7 y^{8} x^{6} + 15 y x^{4}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{7} y^{8} + 3 x^{5} y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{7} y^{8}) + \frac{\partial}{\partial x} (3 x^{5} y)

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

\frac{\partial}{\partial x} (3 x^{5} y) = 15 y x^{4}

= 7 y^{8} x^{6} + 15 y x^{4}

n = 0 \sum \infty \frac{2 n}{n + 3}

x \frac{d y}{d x} + y = - 5 x y^{2}

\int x^{4} - \frac{2}{x} d x

\frac{\partial}{\partial x} ((x + y) ln (x y))

x \to 0 lim (\frac{4}{x ^{5}})