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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

d er i v a t i v e y = \frac{4 x ^{2} + 8 x + 4}{x}

x \to 5 lim (5 - x)

k = 0 \sum \infty \frac{1}{2} \cdot (- 1)^{k}

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