derivative ln((x^2)/(3-x))

Lösung

ableitung von

ln (\frac{x ^{2}}{3 - x})

\frac{6 - x}{x ( - x + 3 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x ^{2}}{3 - x}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{2}}{3 - x}) = \frac{6 x - x ^{2}}{( 3 - x ) ^{2}}

= \frac{1}{\frac{x ^{2}}{3 - x}} \cdot \frac{6 x - x ^{2}}{( 3 - x ) ^{2}}

Vereinfache

\frac{1}{\frac{x ^{2}}{3 - x}} \cdot \frac{6 x - x ^{2}}{( 3 - x ) ^{2}} : \frac{6 - x}{x ( - x + 3 )}

= \frac{6 - x}{x ( - x + 3 )}

\frac{d y}{d x} = 3 y^{\frac{2}{3}}

\frac{\partial}{\partial y} (2 x y^{4} + 2)

x \to 0 lim (\frac{1}{2 x})

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

\int_{\frac{1}{2}}^{1} \frac{4 y + 5}{y ^{2} + y} d y