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} (x^{2} y + 3 x y + y^{2})

x \to \infty lim ((\frac{( 2 x - 3 )}{( 2 x + 5 )})^{2 x + 1})

a re a x = \frac{4}{y}, x = \frac{y}{8}, x = 8 y

\frac{\partial}{\partial x} (\frac{3 x + t}{x - 5 t})

\int_{1}^{2} (8 x^{3} + 3 x^{2}) d x