(\partial)/(\partial s)(arctan(rs))

Lösung

\frac{\partial}{\partial s} (arctan (rs))

\frac{r}{r ^{2} s ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial s} (arctan (rs))

Behandle

r

als Konstante

Wende die Kettenregel an:

\frac{1}{( rs ) ^{2} + 1} \frac{\partial}{\partial s} (rs)

= \frac{1}{( rs ) ^{2} + 1} \frac{\partial}{\partial s} (rs)

\frac{\partial}{\partial s} (rs) = r

= \frac{1}{( rs ) ^{2} + 1} r

Vereinfache

\frac{1}{( rs ) ^{2} + 1} r : \frac{r}{r ^{2} s ^{2} + 1}

= \frac{r}{r ^{2} s ^{2} + 1}

d er i v a t i v e e^{x^{x}}

\int \frac{5 x ^{2}}{( 3 + x ^{3} ) ^{2}} d x

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

y^{^{'}} = 4 y^{2} + x y^{2}, y (0) = 1

\frac{d}{d x} (\frac{sin ( 3 x )}{7 x})