(\partial)/(\partial s)(ln(r^2+s^2+2))

Lösung

\frac{\partial}{\partial s} (ln (r^{2} + s^{2} + 2))

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

Schritte zur Lösung

\frac{\partial}{\partial s} (ln (r^{2} + s^{2} + 2))

Behandle

r

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int e^{x} 25 - e^{2 x} d x

f (x) = x \cdot e^{x}

in v erse l a pl a ce \frac{4}{( s ^{3} + 4 s ^{2} + 8 s )}

\int csc^{4} (x) cos (x) d x

\int x^{4} 3 x^{5} - 5 d x