derivative of \sqrt[5]{x^4}-4/x

Lösung

\frac{d}{d x} (5 x^{4} - \frac{4}{x})

\frac{4 ( x ^{\frac{9}{5}} + 5 )}{5 x ^{\frac{9}{5}} 5 x}

Schritte zur Lösung

\frac{d}{d x} (5 x^{4} - \frac{4}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (\frac{4}{x})

\frac{d}{d x} (5 x^{4}) = \frac{4}{5 x ^{\frac{1}{5}}}

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

= \frac{4}{5 x ^{\frac{1}{5}}} - (- \frac{4}{x ^{2}})

Vereinfache

\frac{4}{5 x ^{\frac{1}{5}}} - (- \frac{4}{x ^{2}}) : \frac{4 ( x ^{\frac{9}{5}} + 5 )}{5 x ^{\frac{9}{5}} 5 x}

= \frac{4 ( x ^{\frac{9}{5}} + 5 )}{5 x ^{\frac{9}{5}} 5 x}

x \to 0 + lim (tan (2 x))

t an g e n t (8 x + 9)^{- 2}

\frac{d}{d x} (x^{3} - 12 x)

\int \frac{8 ( x ^{2} + 4 )}{x ( x ^{2} + 8 )} d x

\frac{d}{d x} (5 x^{3} + 3 x^{2} - 4 x + 1)