derivative of \sqrt[7]{x}-7/x

Lösung

\frac{d}{d x} (7 x - \frac{7}{x})

\frac{x ^{2} + 49 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

Schritte zur Lösung

\frac{d}{d x} (7 x - \frac{7}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7 x) - \frac{d}{d x} (\frac{7}{x})

\frac{d}{d x} (7 x) = \frac{1}{7 x ^{\frac{6}{7}}}

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{x ^{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} - (- \frac{7}{x ^{2}})

Vereinfache

\frac{1}{7 x ^{\frac{6}{7}}} - (- \frac{7}{x ^{2}}) : \frac{x ^{2} + 49 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

= \frac{x ^{2} + 49 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

x = 1 \sum \infty x^{3} e^{- x^{2}}

l a pl a ce t r an s f or m t^{2} e^{- 3 t} sin (4 t)

\int ln (3 x) d x

\frac{d}{d x} ((\frac{x ^{2} + 4}{x ^{2} - 4})^{3})

\int \frac{2 x + 3}{4 x ^{2} - 9} d x