derivative (((3x^2))/((2x+4)))^3

Lösung

ableitung von

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

\frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (\frac{3 x ^{2}}{2 x + 4})^{2} \frac{3 x ( x + 4 )}{2 ( x + 2 ) ^{2}} : \frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

= \frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

\frac{d}{d x} (\frac{- 9 x - 1}{- 6 x + 2})

in v erse l a pl a ce \frac{1}{( s - 1 ) ^{3}}

\int \frac{1 - x}{1 - x} d x

\int cosh^{2} (x - 1) sinh (x - 1) d x

\frac{d}{d x} (ln (x^{l n (x)}))