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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} ((x - 6) (5 x + 1))

\frac{\partial ^{2}}{\partial y ^{2}} (\frac{x y}{x - y})

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

y = (5 - x^{2})^{5}