derivative of x^2-5x+1/(x^{3/2})

Lösung

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

\frac{- 3 + 4 x ^{\frac{7}{2}}}{2 x ^{\frac{5}{2}}} - 5

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (5 x) = 5

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

= 2 x - 5 - \frac{3}{2 x ^{\frac{5}{2}}}

Ziehe Brüche zusammen

- \frac{3}{2 x ^{\frac{5}{2}}} + 2 x : \frac{- 3 + 4 x ^{\frac{7}{2}}}{2 x ^{\frac{5}{2}}}

= \frac{- 3 + 4 x ^{\frac{7}{2}}}{2 x ^{\frac{5}{2}}} - 5

\frac{d y}{d x} = 1 + 4 y^{2}

\int - 4 x (- 2 x^{2} + 2)^{5} d x

d er i v a t i v e y = \frac{e ^{8 x}}{e ^{8 x} + 1}

in v erse l a pl a ce \frac{50}{100 + 0.01 s}

x \to 0 lim (\frac{1}{( x + 1 ) ^{2}})