derivative of (x-1/x ^{5/2})

Lösung

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

\frac{5 ( x ^{2} + 1 ) ( x ^{2} - 1 ) ^{\frac{3}{2}}}{2 x ^{\frac{7}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} \frac{d}{d x} (x - \frac{1}{x})

= \frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} \frac{d}{d x} (x - \frac{1}{x})

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

= \frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} (1 + \frac{1}{x ^{2}})

Vereinfache

\frac{5 ( x - \frac{1}{x} ) ^{\frac{3}{2}}}{2} (1 + \frac{1}{x ^{2}}) : \frac{5 ( x ^{2} + 1 ) ( x ^{2} - 1 ) ^{\frac{3}{2}}}{2 x ^{\frac{7}{2}}}

= \frac{5 ( x ^{2} + 1 ) ( x ^{2} - 1 ) ^{\frac{3}{2}}}{2 x ^{\frac{7}{2}}}

d er i v a t i v e y = (\frac{2 x - 3}{( x ^{2} + 4 ) ^{2}})

s l o p e in t erce pt (1, 4), (4, 1)

d er i v a t i v e y = (2 x + e^{- x^{2}})^{3}

\frac{d P}{d t} = P (a - b P)

a re a y = 2 x, y = 2 x^{2} - 4