derivative of 3/(sqrt(x+8))

Lösung

\frac{d}{d x} (\frac{3}{x + 8})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{x + 8})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{x + 8})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x + 8) = 1

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

Vereinfache

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

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

in v erse l a pl a ce \frac{3 x}{( x - 1 ) ^{4}}

\frac{d}{d x} (arctan (x^{2} + y^{2}))

\frac{d}{d y} (y - 1)

\int (\frac{1}{cos ( x )}) d x

t an g e n t 6 - 5 x^{2}