derivative 1/2 (6t+4)^{-1/2}

Lösung

ableitung von

\frac{1}{2} (6 t + 4)^{- \frac{1}{2}}

- \frac{3}{2 ( 6 t + 4 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{1}{2} (6 t + 4)^{- \frac{1}{2}})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d t} ((6 t + 4)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \frac{d}{d t} (6 t + 4)

= - \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \frac{d}{d t} (6 t + 4)

\frac{d}{d t} (6 t + 4) = 6

= \frac{1}{2} (- \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \cdot 6)

Vereinfache

\frac{1}{2} (- \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \cdot 6) : - \frac{3}{2 ( 6 t + 4 ) ^{\frac{3}{2}}}

= - \frac{3}{2 ( 6 t + 4 ) ^{\frac{3}{2}}}

\int_{0}^{7} \frac{1}{( 6 - 2 x ) ^{\frac{1}{3}}} d x

\frac{d}{d x} (2 x^{3} - 6 x + 5)

x \to 3 lim (\frac{( x )}{x - 3})

t \to 0 lim (arctan (\frac{1}{t}))

\frac{d}{d x} (1 3 x)