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

Lösung

ableitung von

5 x^{4} - \frac{5}{x}

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (5 x^{4}) = \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}}

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

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} - (- \frac{5}{x ^{2}})

Vereinfache

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} + \frac{5}{x ^{2}}

\frac{d}{d x} (7 sin (2 x) + 3 tan (x - 1))

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

t an g e n t y = (x^{3} - 2) (x^{2} - 3 x + 1), (2, - 6)

\frac{d x}{d t} = 7 x

s l o p e 4 x + 3 x^{2}