derivative of ln((3x/(2x+1)))

Lösung

\frac{d}{d x} (ln (\frac{3 x}{2 x + 1}))

\frac{1}{x ( 2 x + 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{3 x}{2 x + 1}))

Wende die Kettenregel an:

\frac{1}{\frac{3 x}{2 x + 1}} \frac{d}{d x} (\frac{3 x}{2 x + 1})

= \frac{1}{\frac{3 x}{2 x + 1}} \frac{d}{d x} (\frac{3 x}{2 x + 1})

\frac{d}{d x} (\frac{3 x}{2 x + 1}) = \frac{3}{( 2 x + 1 ) ^{2}}

= \frac{1}{\frac{3 x}{2 x + 1}} \cdot \frac{3}{( 2 x + 1 ) ^{2}}

Vereinfache

\frac{1}{\frac{3 x}{2 x + 1}} \cdot \frac{3}{( 2 x + 1 ) ^{2}} : \frac{1}{x ( 2 x + 1 )}

= \frac{1}{x ( 2 x + 1 )}

\int \frac{1}{( x + 2 ) ( x + 7 ) ( 2 x - 5 ) ( x + 1 ) ^{2}} d x

a re a y = x e^{- 0.4 x}, x = 5, y = 0

\frac{d}{d x} (2 + sin (x))

x \to 5 + lim (\frac{x - 5}{x - 5})

x \to 0 lim (x ln (x))