derivative of ln(((2x+9^3)/(x^2)))

Lösung

\frac{d}{d x} (ln (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}))

\frac{2 ( x - 9 )}{x ( 2 x + 9 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}))

Wende die Kettenregel an:

\frac{1}{\frac{( 2 x + 9 ) ^{3}}{x ^{2}}} \frac{d}{d x} (\frac{( 2 x + 9 ) ^{3}}{x ^{2}})

= \frac{1}{\frac{( 2 x + 9 ) ^{3}}{x ^{2}}} \frac{d}{d x} (\frac{( 2 x + 9 ) ^{3}}{x ^{2}})

\frac{d}{d x} (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}) = \frac{2 ( 2 x + 9 ) ^{2} ( x - 9 )}{x ^{3}}

= \frac{1}{\frac{( 2 x + 9 ) ^{3}}{x ^{2}}} \cdot \frac{2 ( 2 x + 9 ) ^{2} ( x - 9 )}{x ^{3}}

Vereinfache

\frac{1}{\frac{( 2 x + 9 ) ^{3}}{x ^{2}}} \cdot \frac{2 ( 2 x + 9 ) ^{2} ( x - 9 )}{x ^{3}} : \frac{2 ( x - 9 )}{x ( 2 x + 9 )}

= \frac{2 ( x - 9 )}{x ( 2 x + 9 )}