derivative of-1/(2(x+2^{3/2)})

Lösung

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

\frac{3}{4 ( x + 2 ) ^{\frac{5}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{3}{2 ( x + 2 ) ^{\frac{5}{2}}} \frac{d}{d x} (x + 2)

= - \frac{3}{2 ( x + 2 ) ^{\frac{5}{2}}} \frac{d}{d x} (x + 2)

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

= - \frac{1}{2} (- \frac{3}{2 ( x + 2 ) ^{\frac{5}{2}}} \cdot 1)

Vereinfache

- \frac{1}{2} (- \frac{3}{2 ( x + 2 ) ^{\frac{5}{2}}} \cdot 1) : \frac{3}{4 ( x + 2 ) ^{\frac{5}{2}}}

= \frac{3}{4 ( x + 2 ) ^{\frac{5}{2}}}

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

\int 3 - \frac{1}{3} \cdot (x - 4)^{2} d x

\int_{0}^{2} \frac{x ^{2} - 2}{x + 1} d x

y^{^{'}} = \frac{x ^{2} y + y ^{3}}{x ^{3}}

x \to 0 lim (3 + x^{2} sin (\frac{1}{x}))