derivative of (((3x+1)/(x^2))^3)

Lösung

\frac{d}{d x} ((\frac{( 3 x + 1 )}{x ^{2}})^{3})

\frac{3 ( 3 x + 1 ) ^{2} ( - 3 x - 2 )}{x ^{7}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{( 3 x + 1 )}{x ^{2}})^{3})

Wende die Kettenregel an:

3 (\frac{3 x + 1}{x ^{2}})^{2} \frac{d}{d x} (\frac{3 x + 1}{x ^{2}})

= 3 (\frac{3 x + 1}{x ^{2}})^{2} \frac{d}{d x} (\frac{3 x + 1}{x ^{2}})

\frac{d}{d x} (\frac{3 x + 1}{x ^{2}}) = \frac{- 3 x - 2}{x ^{3}}

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

Vereinfache

3 (\frac{3 x + 1}{x ^{2}})^{2} \frac{- 3 x - 2}{x ^{3}} : \frac{3 ( 3 x + 1 ) ^{2} ( - 3 x - 2 )}{x ^{7}}

= \frac{3 ( 3 x + 1 ) ^{2} ( - 3 x - 2 )}{x ^{7}}

x \to + 0 lim (x (x - [x]))

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

d x - x + y d y = 0

\int e^{17 x} d x

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