derivative of 1/(5x-1)

Lösung

\frac{d}{d x} (\frac{1}{5 x - 1})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{5 x - 1})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e arcsin (x^{4})

d er i v a t i v e f (x) = \frac{7}{x}

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

\frac{d}{d x} (ln (sinh (5 x)))

d er i v a t i v e y = (3 x - 2 x^{2})^{3}