derivative of 7/(sqrt(x+9))

Lösung

\frac{d}{d x} (\frac{7}{x + 9})

- \frac{7}{2 ( x + 9 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{x + 9})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{x + 9})

Wende Exponentenregel an:

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

= 7 \frac{d}{d x} ((x + 9)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 9)

= - \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 9)

\frac{d}{d x} (x + 9) = 1

= 7 (- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

7 (- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{7}{2 ( x + 9 ) ^{\frac{3}{2}}}

= - \frac{7}{2 ( x + 9 ) ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{350}{x ^{2} + y ^{2}})

d er i v a t i v e \frac{1}{3} x^{\frac{3}{2}}

\int_{- \frac{1}{5}}^{\frac{1}{5}} \frac{1}{1 - x ^{2}} d x

x \to 4 - lim (x - 4)

d er i v a t i v e t^{9} cos (t)