derivative of ln(sqrt((9-x/(5+x))))

Lösung

\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

- \frac{7}{( x + 5 ) ( - x + 9 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

Wende die Kettenregel an:

\frac{1}{\frac{9 - x}{5 + x}} \frac{d}{d x} (\frac{9 - x}{5 + x})

= \frac{1}{\frac{9 - x}{5 + x}} \frac{d}{d x} (\frac{9 - x}{5 + x})

\frac{d}{d x} (\frac{9 - x}{5 + x}) = - \frac{7}{- x + 9 ( x + 5 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{9 - x}{5 + x}} (- \frac{7}{- x + 9 ( x + 5 ) ^{\frac{3}{2}}})

Vereinfache

\frac{1}{\frac{9 - x}{5 + x}} (- \frac{7}{- x + 9 ( x + 5 ) ^{\frac{3}{2}}}) : - \frac{7}{( x + 5 ) ( - x + 9 )}

= - \frac{7}{( x + 5 ) ( - x + 9 )}

d er i v a t i v e - 9 x^{2}

\frac{d}{d x} (arccos (cos (x)))

im pl i c i t \frac{d y}{d x}, x y = x - 2 y

\frac{d y}{d x} = \frac{( x - 3 )}{y - 4}

\int \frac{289}{x ^{3} - 17 x ^{2}} d x