d/(dz)(ln(sqrt((b^2-z^2)/(b^2+z^2))))

Lösung

\frac{d}{d z} (ln (\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}))

- \frac{2 b ^{2} z}{( z ^{2} + b ^{2} ) ( - z ^{2} + b ^{2} )}

Schritte zur Lösung

\frac{d}{d z} (ln (\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}))

Wende die Kettenregel an:

\frac{1}{\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}} \frac{d}{d z} (\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}})

= \frac{1}{\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}} \frac{d}{d z} (\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}})

\frac{d}{d z} (\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}) = - \frac{2 b ^{2} z}{- z ^{2} + b ^{2} ( z ^{2} + b ^{2} ) ^{\frac{3}{2}}}

= \frac{1}{\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}} (- \frac{2 b ^{2} z}{- z ^{2} + b ^{2} ( z ^{2} + b ^{2} ) ^{\frac{3}{2}}})

Vereinfache

\frac{1}{\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}} (- \frac{2 b ^{2} z}{- z ^{2} + b ^{2} ( z ^{2} + b ^{2} ) ^{\frac{3}{2}}}) : - \frac{2 b ^{2} z}{( z ^{2} + b ^{2} ) ( - z ^{2} + b ^{2} )}

= - \frac{2 b ^{2} z}{( z ^{2} + b ^{2} ) ( - z ^{2} + b ^{2} )}

y^{^{''}} + 9 y = 4 csc^{2} (3 t)

\int 6 - 4 x - 4 x^{2} d x

\frac{d}{d x} (\frac{d y}{d x}) = 1

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

\frac{d y}{d x} = sin (x) y + e^{x}