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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

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

\int x^{3} x^{2} + 9 d x

\frac{\partial}{\partial x} (sin (π (6 x - y)))

d er i v a t i v e arctan (\frac{1 + t}{1 - t})