derivative 4t^{(-1)/8}+5ln(t)+ln(5)

Lösung

ableitung von

4 t^{\frac{- 1}{8}} + 5 ln (t) + ln (5)

\frac{10 t ^{\frac{9}{8}} - t}{2 t ^{\frac{17}{8}}}

Schritte zur Lösung

\frac{d}{d t} (4 t^{\frac{- 1}{8}} + 5 ln (t) + ln (5))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (4 t^{\frac{- 1}{8}}) + \frac{d}{d t} (5 ln (t)) + \frac{d}{d t} (ln (5))

\frac{d}{d t} (4 t^{\frac{- 1}{8}}) = - \frac{1}{2 t ^{\frac{9}{8}}}

\frac{d}{d t} (5 ln (t)) = \frac{5}{t}

\frac{d}{d t} (ln (5)) = 0

= - \frac{1}{2 t ^{\frac{9}{8}}} + \frac{5}{t} + 0

Vereinfache

- \frac{1}{2 t ^{\frac{9}{8}}} + \frac{5}{t} + 0 : \frac{10 t ^{\frac{9}{8}} - t}{2 t ^{\frac{17}{8}}}

= \frac{10 t ^{\frac{9}{8}} - t}{2 t ^{\frac{17}{8}}}

t an g e n t f (x) = 3 x^{2} - 4 x + 1

\frac{d}{d x} (\frac{9 - sec ( x )}{tan ( x )})

\int (x^{3} + 5) d x

\int e^{\frac{t}{5}} d t

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