derivative of 4sqrt(x^5)+2/(sqrt(x))

Lösung

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

\frac{- 1 + 10 x ^{3}}{x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (4 x^{5}) = 10 x^{\frac{3}{2}}

\frac{d}{d x} (\frac{2}{x}) = - \frac{1}{x ^{\frac{3}{2}}}

= 10 x^{\frac{3}{2}} - \frac{1}{x ^{\frac{3}{2}}}

Vereinfache

10 x^{\frac{3}{2}} - \frac{1}{x ^{\frac{3}{2}}} : \frac{- 1 + 10 x ^{3}}{x ^{\frac{3}{2}}}

= \frac{- 1 + 10 x ^{3}}{x ^{\frac{3}{2}}}

\int 7 \frac{sin ( 2 x )}{sin ( x )} d x

a re a x^{2}, 3

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

\int 2 x (x^{2} - 3)^{3} d x

\int x^{k} d x