derivative of 2/(ln(10x^3))

Lösung

\frac{d}{d x} (\frac{2}{ln ( 10 ) x ^{3}})

- \frac{6}{ln ( 10 ) x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{ln ( 10 ) x ^{3}})

Entferne die Konstante:

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

= \frac{2}{ln ( 10 )} \frac{d}{d x} (\frac{1}{x ^{3}})

Wende Exponentenregel an:

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

= \frac{2}{ln ( 10 )} \frac{d}{d x} (x^{- 3})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{2}{ln ( 10 )} (- 3 x^{- 3 - 1})

Vereinfache

\frac{2}{ln ( 10 )} (- 3 x^{- 3 - 1}) : - \frac{6}{ln ( 10 ) x ^{4}}

= - \frac{6}{ln ( 10 ) x ^{4}}

\int_{4}^{7} \frac{1}{x ^{2} - 16} d x

\frac{d}{d x} (2 x)

t an g e n t f (x) = x^{2} - 2 x - 6, at x = - 2

x \to 8 lim (\frac{4}{x - 8})

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