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

Lösung

ableitung von

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

x \to 3 lim (\frac{x - 3}{1 + x})

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

t an g e n t \frac{2}{3} x^{3} + 4 x^{2} + 6 x - 5

\int \frac{196}{w ^{2} 49 - w ^{2}} d w

\int \frac{1}{2 x + 3} d x