derivative of 2/(sqrt(x^2-3))

Lösung

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

- \frac{2 x}{( x ^{2} - 3 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 (- \frac{1}{2 ( x ^{2} - 3 ) ^{\frac{3}{2}}} \cdot 2 x) : - \frac{2 x}{( x ^{2} - 3 ) ^{\frac{3}{2}}}

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

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

d er i v a t i v e y = 34 (3 p + 1) - \frac{2}{5}, p > 0

(x + 1)^{^{'}}

\int \frac{2 x - 4 + 8 x}{x} d x

x \to 1 lim (\frac{x ^{2} - 3 x}{x})