derivative f(x)= 7/((x^2-10)^4)

Lösung

ableitung von

f (x) = \frac{7}{( x ^{2} - 10 ) ^{4}}

- \frac{56 x}{( x ^{2} - 10 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{( x ^{2} - 10 ) ^{4}})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{( x ^{2} - 10 ) ^{4}})

Wende Exponentenregel an:

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

= 7 \frac{d}{d x} ((x^{2} - 10)^{- 4})

Wende die Kettenregel an:

- \frac{4}{( x ^{2} - 10 ) ^{5}} \frac{d}{d x} (x^{2} - 10)

= - \frac{4}{( x ^{2} - 10 ) ^{5}} \frac{d}{d x} (x^{2} - 10)

\frac{d}{d x} (x^{2} - 10) = 2 x

= 7 (- \frac{4}{( x ^{2} - 10 ) ^{5}} \cdot 2 x)

Vereinfache

7 (- \frac{4}{( x ^{2} - 10 ) ^{5}} \cdot 2 x) : - \frac{56 x}{( x ^{2} - 10 ) ^{5}}

= - \frac{56 x}{( x ^{2} - 10 ) ^{5}}

d er i v a t i v e f (x) = \frac{4}{x} - 16 sec (x)

\int - 3 x^{4} - 6 x^{2} + 8 d x

x \to 0 lim (x csc (π x))

x \to \frac{1}{3} lim (x^{4})

x \to + 0 + lim (x^{x})