d/(d{r)}(({r})/(sqrt({r)^2+5)})

Lösung

\frac{d}{d r} (\frac{r}{r ^{2} + 5})

\frac{5}{( r ^{2} + 5 ) r ^{2} + 5}

Schritte zur Lösung

\frac{d}{d r} (\frac{r}{r ^{2} + 5})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d r} ( r ) r ^{2} + 5 - \frac{d}{d r} ( r ^{2} + 5 ) r}{( r ^{2} + 5 ) ^{2}}

\frac{d}{d r} (r) = 1

\frac{d}{d r} (r^{2} + 5) = \frac{r}{r ^{2} + 5}

= \frac{1 \cdot r ^{2} + 5 - \frac{r}{r ^{2} + 5} r}{( r ^{2} + 5 ) ^{2}}

Vereinfache

\frac{1 \cdot r ^{2} + 5 - \frac{r}{r ^{2} + 5} r}{( r ^{2} + 5 ) ^{2}} : \frac{5}{( r ^{2} + 5 ) r ^{2} + 5}

= \frac{5}{( r ^{2} + 5 ) r ^{2} + 5}

t \to 3 lim (\frac{2 t - 3}{t - 3})

s l o p e y = 5 sec (x) - 10 cos (x), (\frac{π}{3}, 5)

d er i v a t i v e y = arcsin (3 5 x)

x \to 1 lim (2 3 x^{2} + 1)

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