derivative of (x/5-5/x ^5)

Lösung

\frac{d}{d x} ((\frac{x}{5} - \frac{5}{x})^{5})

(\frac{x}{5} - \frac{5}{x})^{4} + \frac{( x ^{2} - 25 ) ^{4}}{25 x ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x}{5} - \frac{5}{x})^{5})

Wende die Kettenregel an:

5 (\frac{x}{5} - \frac{5}{x})^{4} \frac{d}{d x} (\frac{x}{5} - \frac{5}{x})

= 5 (\frac{x}{5} - \frac{5}{x})^{4} \frac{d}{d x} (\frac{x}{5} - \frac{5}{x})

\frac{d}{d x} (\frac{x}{5} - \frac{5}{x}) = \frac{1}{5} + \frac{5}{x ^{2}}

= 5 (\frac{x}{5} - \frac{5}{x})^{4} (\frac{1}{5} + \frac{5}{x ^{2}})

Vereinfache

5 (\frac{x}{5} - \frac{5}{x})^{4} (\frac{1}{5} + \frac{5}{x ^{2}}) : (\frac{x}{5} - \frac{5}{x})^{4} + \frac{( x ^{2} - 25 ) ^{4}}{25 x ^{6}}

= (\frac{x}{5} - \frac{5}{x})^{4} + \frac{( x ^{2} - 25 ) ^{4}}{25 x ^{6}}

\int_{0}^{2} (2 x - 3) (4 x^{2} + 1) d x

t an g e n t f (x) = 4 x^{2} + 4 x - 2, at x = - 1

\frac{d}{d x} ((x^{3} + 5) e^{x})

\int cos (4 x) 2 - sin (4 x) d x

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