derivative 4sqrt(x)-3/(x^6)

Lösung

ableitung von

4 x - \frac{3}{x ^{6}}

\frac{2 ( x ^{\frac{13}{2}} + 9 )}{x ^{\frac{13}{2}} x}

Schritte zur Lösung

\frac{d}{d x} (4 x - \frac{3}{x ^{6}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x) - \frac{d}{d x} (\frac{3}{x ^{6}})

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

\frac{d}{d x} (\frac{3}{x ^{6}}) = - \frac{18}{x ^{7}}

= \frac{2}{x} - (- \frac{18}{x ^{7}})

Vereinfache

\frac{2}{x} - (- \frac{18}{x ^{7}}) : \frac{2 ( x ^{\frac{13}{2}} + 9 )}{x ^{\frac{13}{2}} x}

= \frac{2 ( x ^{\frac{13}{2}} + 9 )}{x ^{\frac{13}{2}} x}

\int 2 x^{2} - 4 d x

\int \frac{4}{x + 4 + x} d x

x \to - 1 lim (4 x^{3} - 2 m)

x \to 0 - lim (\frac{x ^{2}}{2} - \frac{1}{x})

\int \frac{1}{sec ( x ) + 1} d x