derivative of ln(((x+2)/(x^2)))

Lösung

\frac{d}{d x} (ln (\frac{( x + 2 )}{x ^{2}}))

\frac{- x - 4}{x ( x + 2 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{( x + 2 )}{x ^{2}}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x + 2}{x ^{2}}) = \frac{- x - 4}{x ^{3}}

= \frac{1}{\frac{x + 2}{x ^{2}}} \cdot \frac{- x - 4}{x ^{3}}

Vereinfache

\frac{1}{\frac{x + 2}{x ^{2}}} \cdot \frac{- x - 4}{x ^{3}} : \frac{- x - 4}{x ( x + 2 )}

= \frac{- x - 4}{x ( x + 2 )}

x \to 1 + lim (\frac{1}{1 - x ^{2}})

d er i v a t i v e f (x) = x e^{x^{2}}

d er i v a t i v e \frac{5 x ^{2} tan ( x )}{sec ( x )}

\int \frac{x ^{2}}{x - 9} d x

a re a 2 - x^{2}, x^{2}