derivative f(x)=ln((x^2)/(x^2+4))

Lösung

ableitung von

f (x) = ln (\frac{x ^{2}}{x ^{2} + 4})

\frac{8}{x ( x ^{2} + 4 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x ^{2}}{x ^{2} + 4}))

Wende die Kettenregel an:

\frac{1}{\frac{x ^{2}}{x ^{2} + 4}} \frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 4})

= \frac{1}{\frac{x ^{2}}{x ^{2} + 4}} \frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 4})

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 4}) = \frac{8 x}{( x ^{2} + 4 ) ^{2}}

= \frac{1}{\frac{x ^{2}}{x ^{2} + 4}} \cdot \frac{8 x}{( x ^{2} + 4 ) ^{2}}

Vereinfache

\frac{1}{\frac{x ^{2}}{x ^{2} + 4}} \cdot \frac{8 x}{( x ^{2} + 4 ) ^{2}} : \frac{8}{x ( x ^{2} + 4 )}

= \frac{8}{x ( x ^{2} + 4 )}

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