derivative of kaln((x+d/(x-d)))

Lösung

\frac{d}{d x} (ka ln (\frac{x + d}{x - d}))

- \frac{2 ak d}{( x + d ) ( x - d )}

Schritte zur Lösung

\frac{d}{d x} (ka ln (\frac{x + d}{x - d}))

Behandle

a, k, d

als Konstante

Entferne die Konstante:

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

= ka \frac{d}{d x} (ln (\frac{x + d}{x - d}))

Wende die Kettenregel an:

\frac{1}{\frac{x + d}{x - d}} \frac{d}{d x} (\frac{x + d}{x - d})

= \frac{1}{\frac{x + d}{x - d}} \frac{d}{d x} (\frac{x + d}{x - d})

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

= ka \frac{1}{\frac{x + d}{x - d}} (- \frac{2 d}{( x - d ) ^{2}})

Vereinfache

ka \frac{1}{\frac{x + d}{x - d}} (- \frac{2 d}{( x - d ) ^{2}}) : - \frac{2 ak d}{( x + d ) ( x - d )}

= - \frac{2 ak d}{( x + d ) ( x - d )}

t a y l or \frac{1}{2} cos (7 x)

\frac{d y}{d x} = y^{2} + 2 y

\frac{\partial}{\partial x} (e^{i x})

y^{^{'}} + y = t

\frac{d}{d x} (\frac{x}{x + 3})