(\partial)/(\partial x)((x^2+y^2)/(z^2))

Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{z ^{2}})

\frac{2 x}{z ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{z ^{2}})

Behandle

y, z

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{z ^{2}} \frac{\partial}{\partial x} (x^{2} + y^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{1}{z ^{2}} (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (y^{2}))

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

\frac{\partial}{\partial x} (y^{2}) = 0

= \frac{1}{z ^{2}} (2 x + 0)

Vereinfache

\frac{1}{z ^{2}} (2 x + 0) : \frac{2 x}{z ^{2}}

= \frac{2 x}{z ^{2}}

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

h \to 0 lim (- 2 x - h + 8)

x \to 1 lim (\frac{x + 1}{x ^{3} - 1})

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

\frac{d P}{d t} = P - P^{2}