derivative f(t)=sqrt(t)-1/(sqrt(t))

Lösung

ableitung von

f (t) = t - \frac{1}{t}

\frac{1}{2 t} + \frac{1}{2 t ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d t} (t - \frac{1}{t})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (t) - \frac{d}{d t} (\frac{1}{t})

\frac{d}{d t} (t) = \frac{1}{2 t}

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

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

Vereinfache

= \frac{1}{2 t} + \frac{1}{2 t ^{\frac{3}{2}}}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 2} d x

d er i v a t i v e \frac{2 x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + 6

x \to 2 lim (ln (x))

x \to 58 lim (\frac{x + 6 - 8}{x - 58})

d er i v a t i v e y = 2 x e^{- k x}