(\partial)/(\partial {g)}(2pisqrt(l/({g))})

Lösung

\frac{\partial}{\partial g} (2 π \frac{l}{g})

- \frac{π l}{g ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial g} (2 π \frac{l}{g})

Entferne die Konstante:

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

= 2 π \frac{\partial}{\partial g} (\frac{l}{g})

Wende die Kettenregel an:

\frac{1}{2 \frac{l}{g}} \frac{\partial}{\partial g} (\frac{l}{g})

= \frac{1}{2 \frac{l}{g}} \frac{\partial}{\partial g} (\frac{l}{g})

\frac{\partial}{\partial g} (\frac{l}{g}) = - \frac{l}{g ^{2}}

= 2 π \frac{1}{2 \frac{l}{g}} (- \frac{l}{g ^{2}})

Vereinfache

2 π \frac{1}{2 \frac{l}{g}} (- \frac{l}{g ^{2}}) : - \frac{π l}{g ^{\frac{3}{2}}}

= - \frac{π l}{g ^{\frac{3}{2}}}

l a pl a ce t r an s f or m (t - 1)^{2}

\frac{d}{d x} (\frac{x ^{3}}{2})

x \to 2 + lim (4 x^{2} - 2 x + 3)

t an g e n t f (x) = 7 x, at x = 25

d er i v a t i v e ln (x^{\frac{3}{2}})