derivative of-1/(4(1+x^{3/2)})

Lösung

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

\frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{4} (- \frac{3}{2 ( 1 + x ) ^{\frac{5}{2}}} \cdot 1) : \frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}}

= \frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}}

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

n = 1 \sum \infty (x - 4)^{n}

\frac{d}{d x} (ln (x x^{2} - 9))

x \to \infty lim (15)

d er i v a t i v e f (x) = \frac{x}{x + 9}