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

Lösung

ableitung von

y = (\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}}

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

l a pl a ce t r an s f or m f (t) = 2 (1 - e^{- 5 t})

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

d er i v a t i v e y = ln (x - 4)

l a pl a ce t r an s f or m - 5 e^{2 t}