derivative 1/2 (8t+3)^{-1/2}

Lösung

ableitung von

\frac{1}{2} (8 t + 3)^{- \frac{1}{2}}

- \frac{2}{( 8 t + 3 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{1}{2} (8 t + 3)^{- \frac{1}{2}})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d t} ((8 t + 3)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 8 t + 3 ) ^{\frac{3}{2}}} \frac{d}{d t} (8 t + 3)

= - \frac{1}{2 ( 8 t + 3 ) ^{\frac{3}{2}}} \frac{d}{d t} (8 t + 3)

\frac{d}{d t} (8 t + 3) = 8

= \frac{1}{2} (- \frac{1}{2 ( 8 t + 3 ) ^{\frac{3}{2}}} \cdot 8)

Vereinfache

\frac{1}{2} (- \frac{1}{2 ( 8 t + 3 ) ^{\frac{3}{2}}} \cdot 8) : - \frac{2}{( 8 t + 3 ) ^{\frac{3}{2}}}

= - \frac{2}{( 8 t + 3 ) ^{\frac{3}{2}}}

\frac{d}{d x} (f (x) \cdot f (x) \cdot f (x))

y^{^{'}} - \frac{8}{x} y = y^{3} \frac{1}{x ^{12}}

a re a y = x^{2}, x = y^{2}

3 x y^{^{'}} - 15 y = x^{- 1}

n = 9 \sum \infty (\frac{1}{7})^{n}