derivative f(x)=((-7)/(sqrt(7x^2+1)))

Lösung

ableitung von

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

\frac{49 x}{( 7 x ^{2} + 1 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Vereinfache

\frac{- 7}{7 x ^{2} + 1} : - \frac{7}{7 x ^{2} + 1}

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{2} + 1)

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

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= - 7 (- \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 14 x)

Vereinfache

- 7 (- \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 14 x) : \frac{49 x}{( 7 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{49 x}{( 7 x ^{2} + 1 ) ^{\frac{3}{2}}}

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