derivative 1/2 (2t+1)^{-1/2}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2} (- \frac{1}{2 ( 2 t + 1 ) ^{\frac{3}{2}}} \cdot 2) : - \frac{1}{2 ( 2 t + 1 ) ^{\frac{3}{2}}}

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

roo t s a x^{2} e^{2 x}

n = 1 \sum \infty \frac{6}{n ^{2} + 2 n}

\int_{1}^{10} \frac{21}{x ^{3}} d x

x \to - 1 lim (\frac{4}{( x + 1 ) ^{2}})

\frac{d}{d x} (sin^{2} (\frac{x ^{2} + 1}{x}))