derivative of 4/(x+2sqrt(x))

Lösung

\frac{d}{d x} (\frac{4}{x + 2 x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{x + 2 x})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{1}{x + 2 x})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} (\frac{g ( x )}{x})

\int - 4 y^{2} d y

\frac{\partial}{\partial x} ((x + y)^{3})

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