derivative y= 1/t+1/(t^2)-1/(sqrt(t))

Lösung

ableitung von

y = \frac{1}{t} + \frac{1}{t ^{2}} - \frac{1}{t}

\frac{- 2 t ^{\frac{5}{2}} - 4 t ^{\frac{3}{2}} + t ^{3}}{2 t ^{\frac{9}{2}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

Vereinfache

- \frac{1}{t ^{2}} - \frac{2}{t ^{3}} - (- \frac{1}{2 t ^{\frac{3}{2}}}) : \frac{- 2 t ^{\frac{5}{2}} - 4 t ^{\frac{3}{2}} + t ^{3}}{2 t ^{\frac{9}{2}}}

= \frac{- 2 t ^{\frac{5}{2}} - 4 t ^{\frac{3}{2}} + t ^{3}}{2 t ^{\frac{9}{2}}}

s im pl i f y (x^{2} + a^{2})^{e^{x^{2}}}

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