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}}

x \to - 1 f lim (x)

a re a g (x) = x^{2}, g (x) = x^{k} 0, 1

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

x \frac{d y}{d x} + 4 y = x^{3} - x

a re a \frac{1}{( 16 x ^{2} )}, x, \frac{x}{6}