derivative of ((3x^2-2/(2x+3))^3)

Lösung

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

\frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{3 x ^{2} - 2}{2 x + 3}) = \frac{6 x ^{2} + 18 x + 4}{( 2 x + 3 ) ^{2}}

= 3 (\frac{3 x ^{2} - 2}{2 x + 3})^{2} \frac{6 x ^{2} + 18 x + 4}{( 2 x + 3 ) ^{2}}

Vereinfache

3 (\frac{3 x ^{2} - 2}{2 x + 3})^{2} \frac{6 x ^{2} + 18 x + 4}{( 2 x + 3 ) ^{2}} : \frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

= \frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

\frac{\partial}{\partial x} (3 x^{2} - y^{3} + x - 1)

\int \frac{( ln ( x ^{8} ) )}{x} d x

\int sin (\frac{1}{3}) x d x

\frac{\partial}{\partial x} (9 y e^{x} - ln (z))

in v erse l a pl a ce \frac{s + 2}{s ^{2} + 2 s + 5}