derivative of 2/((x+2^3))

Lösung

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

- \frac{6}{( x + 2 ) ^{4}}

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})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 (- \frac{3}{( x + 2 ) ^{4}} \cdot 1) : - \frac{6}{( x + 2 ) ^{4}}

= - \frac{6}{( x + 2 ) ^{4}}

\frac{\partial}{\partial x} (7 - x^{2} + x y - 2 y^{2})

\frac{d}{d x} (6 x^{- 2})

t an g e n t 4 x - x^{2}, (1.3)

d er i v a t i v e f (x) = 5 x^{4} - 6 x^{2} + 1

\frac{\partial}{\partial x} (2 x y - 3)