derivative of ln((8x/(x+5)))

Lösung

\frac{d}{d x} (ln (\frac{8 x}{x + 5}))

\frac{5}{x ( x + 5 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{8 x}{x + 5}))

Wende die Kettenregel an:

\frac{1}{\frac{8 x}{x + 5}} \frac{d}{d x} (\frac{8 x}{x + 5})

= \frac{1}{\frac{8 x}{x + 5}} \frac{d}{d x} (\frac{8 x}{x + 5})

\frac{d}{d x} (\frac{8 x}{x + 5}) = \frac{40}{( x + 5 ) ^{2}}

= \frac{1}{\frac{8 x}{x + 5}} \cdot \frac{40}{( x + 5 ) ^{2}}

Vereinfache

\frac{1}{\frac{8 x}{x + 5}} \cdot \frac{40}{( x + 5 ) ^{2}} : \frac{5}{x ( x + 5 )}

= \frac{5}{x ( x + 5 )}

x \to 5 lim (\frac{1}{( x - 5 ) ^{3}})

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{8}})

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

y^{^{'}} = 1 - \frac{y}{20}

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y