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}}

x d y - y d x = (x y)^{\frac{1}{2}} d x

t an g e n t f (x) = 7 cos (x), at (\frac{2 π}{3})

x \to 1 lim (\frac{2 - x}{x - 1})

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

s l o p e (10.1) (5.2)