derivative of ln((6-x/(6+x)))

Lösung

\frac{d}{d x} (ln (\frac{6 - x}{6 + x}))

- \frac{12}{( - x + 6 ) ( x + 6 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{6 - x}{6 + x}))

Wende die Kettenregel an:

\frac{1}{\frac{6 - x}{6 + x}} \frac{d}{d x} (\frac{6 - x}{6 + x})

= \frac{1}{\frac{6 - x}{6 + x}} \frac{d}{d x} (\frac{6 - x}{6 + x})

\frac{d}{d x} (\frac{6 - x}{6 + x}) = - \frac{12}{( 6 + x ) ^{2}}

= \frac{1}{\frac{6 - x}{6 + x}} (- \frac{12}{( 6 + x ) ^{2}})

Vereinfache

\frac{1}{\frac{6 - x}{6 + x}} (- \frac{12}{( 6 + x ) ^{2}}) : - \frac{12}{( - x + 6 ) ( x + 6 )}

= - \frac{12}{( - x + 6 ) ( x + 6 )}

\frac{\partial}{\partial x} (y - 2 x)

\int 12 sin^{2} (x) d x

x^{^{''}} + x^{^{'}} + 2 x = 4 e^{2 t}

\frac{d}{d x} (x^{x^{\frac{1}{2}}})

f (x) = 9 e^{x}