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

Lösung

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

- \frac{3 ( x + 1 ) ^{2}}{x ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (\frac{x + 1}{x})^{2} (- \frac{1}{x ^{2}}) : - \frac{3 ( x + 1 ) ^{2}}{x ^{4}}

= - \frac{3 ( x + 1 ) ^{2}}{x ^{4}}

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

t an g e n t f (x) = (13 x - 1)^{- \frac{1}{3}}, at x = 5

d er i v a t i v e \frac{t}{( t - 9 ) ^{2}}

25 y^{^{''}} + 30 y^{^{'}} + 9 y = 0

\frac{\partial}{\partial x} (2 x^{0.3} y^{0.3} + 1)