derivative f(x)=(x+1/(\sqrt[3]{x)})^2

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

x \to \infty lim (e^{- 6 x} cos (x))

x y^{2} y^{^{'}} = y^{3} - 3 x^{3}, y (1) = 6

a re a x = 8 y^{2}, x = 2 + 6 y^{2}

x \to - \infty lim (1 0^{x})

\frac{\partial}{\partial x} (x^{- 3} y^{2} + x y^{2} + 5 x y)