derivative y=ln(sqrt((a+bx)/(a-bx)))

Lösung

ableitung von

y = ln (\frac{a + b x}{a - b x})

\frac{ab}{( - b x + a ) ( b x + a )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{a + b x}{a - b x}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{a + b x}{a - b x}) = \frac{ab}{b x + a ( - b x + a ) ^{\frac{3}{2}}}

= \frac{1}{\frac{a + b x}{a - b x}} \cdot \frac{ab}{b x + a ( - b x + a ) ^{\frac{3}{2}}}

Vereinfache

\frac{1}{\frac{a + b x}{a - b x}} \cdot \frac{ab}{b x + a ( - b x + a ) ^{\frac{3}{2}}} : \frac{ab}{( - b x + a ) ( b x + a )}

= \frac{ab}{( - b x + a ) ( b x + a )}

t a y l or cos (x + 1)

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6 (t + 1) \frac{d y}{d t} - 5 y = 5 t

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\frac{d}{d x} (x^{4} + y^{4} + z^{4} - 4 x y z)