derivative of 7/(sqrt(x+5))

Lösung

\frac{d}{d x} (\frac{7}{x + 5})

- \frac{7}{2 ( x + 5 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{x + 5})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{x + 5})

Wende Exponentenregel an:

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

= 7 \frac{d}{d x} ((x + 5)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 5)

= - \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = 1

= 7 (- \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

7 (- \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{7}{2 ( x + 5 ) ^{\frac{3}{2}}}

= - \frac{7}{2 ( x + 5 ) ^{\frac{3}{2}}}

y^{^{'}} = \frac{( x + y ) ^{2}}{2 x ^{2}}

t an g e n t f (x) = 3 x^{3} + 2 x^{2} + 1, at x = - 1

x \to - 2 - lim (\frac{- 3}{x + 2})

x \to 0 lim (ln (\frac{7}{x ^{2}}))

\frac{d}{d x} (\frac{5}{3 x - 4})