derivative of 5/(2x+1)

Lösung

\frac{d}{d x} (\frac{5}{2 x + 1})

- \frac{10}{( 2 x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{2 x + 1})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

5 (- \frac{1}{( 2 x + 1 ) ^{2}} \cdot 2) : - \frac{10}{( 2 x + 1 ) ^{2}}

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

d er i v a t i v e f (x) = 3 sin (x) + 2 cos (x)

\frac{d}{d x} (sinh^{3} (2 x))

\int \frac{2 x ^{2} - 25 x - 33}{( x + 1 ) ^{2} ( x - 5 )} d x

3 e^{5 x} \frac{d y}{d x} = \frac{- 25 x}{y ^{2}}, y (0) = 1

x \to 2 lim ((x - 1) (x + 1))