derivative y=((2x^2)/(6-x))^3

Lösung

ableitung von

y = (\frac{2 x ^{2}}{6 - x})^{3}

\frac{24 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{2 x ^{2}}{6 - x})^{3})

Wende die Kettenregel an:

3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{d}{d x} (\frac{2 x ^{2}}{6 - x})

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

\frac{d}{d x} (\frac{2 x ^{2}}{6 - x}) = \frac{2 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}}

= 3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{2 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}}

Vereinfache

3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{2 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}} : \frac{24 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

= \frac{24 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

\int \frac{x ^{3} + 2 x ^{2} + 5 x + 1}{x ^{2} + 2 x + 5} d x

t an g e n t f (x) = \frac{2}{x - 2}, at x = 4

a re a x^{2} - 6, - 2 x + 9, - 5, 3

\frac{d}{d x} (3 3 x + 6)

\int \frac{9}{1 + e ^{2 x}} d x