derivative of 7/(sqrt(x+8))

Lösung

\frac{d}{d x} (\frac{7}{x + 8})

- \frac{7}{2 ( x + 8 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{x + 8})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{x + 8})

Wende Exponentenregel an:

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

= 7 \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

= 7 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

7 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{7}{2 ( x + 8 ) ^{\frac{3}{2}}}

= - \frac{7}{2 ( x + 8 ) ^{\frac{3}{2}}}

\frac{d}{d x} (A e^{- 3 x})

\int \frac{1}{ln ^{2} ( x )} d x

a re a 2 x^{2} + 3, (- 1, 2)

\frac{d}{d x} ((1 + cos^{2} (x))^{6})

\frac{d}{d t} (15 t^{2})