derivative of (10/(sqrt(x^2-4x+1)))

Lösung

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

- \frac{5 ( 2 x - 4 )}{( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} - 4 x + 1)

= - \frac{1}{2 ( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} - 4 x + 1)

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

= 10 (- \frac{1}{2 ( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}} (2 x - 4))

Vereinfache

10 (- \frac{1}{2 ( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}} (2 x - 4)) : - \frac{5 ( 2 x - 4 )}{( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}}

= - \frac{5 ( 2 x - 4 )}{( x ^{2} - 4 x + 1 ) ^{\frac{3}{2}}}

\int 4 x - 4 d x

d er i v a t i v e 2 (x - 1)

\int e^{2 y - y^{2}} d y

3 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

\int \frac{x + 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x