MathGymOS/ Analysis/ Differentialrechnung/ Ableitung ganzrationaler Funktionen/ Übungsaufgaben/ Lösungen

Hier sind die Lösungen der Übungsaufgaben zum Ableiten.

Allgemeines Ableiten

$f (x) = x^{4} + x^{2}; f^{'} (x) = 4 x^{3} + 2 x$
$f (x) = x^{3} - x^{\frac{1}{7}}; f^{'} (x) = 3 x^{2} - \frac{1}{7} x^{- \frac{6}{7}}$
$f (x) = x^{2} + 6; f^{'} (x) = 2 x$
$f (x) = 3 + 4; f^{'} (x) = 0$

$f (x) = x^{3} + x^{2}; f^{'} (x) = 3 x^{2} + 2 x; f^{″} (x) = 6 x + 2$
$f (x) = 2 x^{4} - 4 x; f^{'} (x) = 8 x^{3} - 4; f^{″} (x) = 24 x^{2}$
$f (x) = - 5 x^{3} + x - 6; f^{'} (x) = - 15 x^{2} + 1; f^{″} (x) = - 30 x$
$f (x) = \frac{2}{4} x^{4} + x^{2}; f^{'} (x) = 2 x^{3} + 2 x; f^{″} (x) = 6 x^{2} + 2$
$f (x) = - \frac{3}{7} x^{- 4} + 7 x^{2} - \frac{2}{3}; f^{'} (x) = \frac{12}{7} x^{- 5} + 14 x; f^{″} (x) = - \frac{60}{7} x^{- 6} + 14$
$f (x) = 2 x^{3} + 1 \frac{1}{2} x^{7}; f^{'} (x) = 6 x^{2} + \frac{21}{2} x^{6}; f^{″} (x) = 12 x + 63 x^{5}$
$f (x) = 0.2 x^{\frac{2}{5}}; f^{'} (x) = \frac{2}{25} x^{- \frac{3}{5}}; f^{″} (x) = - \frac{6}{125} x^{- \frac{8}{5}}$
$f (x) = x^{\frac{5}{7}} + x^{- 3}; f^{'} (x) = \frac{5}{7} x^{- \frac{2}{7}} - 3 x^{- 4}; f^{″} (x) = - \frac{10}{49} x^{- \frac{9}{7}} + 12 x^{- 5}$
$f (x) = x + 6^{4}; f^{'} (x) = 1; f^{″} (x) = 0$
$f (x) = - \frac{1}{6} x^{5} + 4 x^{4} - \frac{6}{7} x^{- 2} + 2 x^{\frac{1}{3}} - x + \frac{23}{56}; f^{'} (x) = - \frac{5}{6} x^{4} + 16 x^{3} + \frac{12}{7} x^{- 3} + \frac{2}{3} x^{- \frac{2}{3}} - 1;$
$f^{″} (x) = - \frac{10}{3} x^{3} + 48 x^{2} - \frac{36}{7} x^{- 4} - \frac{4}{9} x^{- \frac{5}{3}}$