derivative of 3/(4(1-x^{5/2)})

Lösung

\frac{d}{d x} (\frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}})

\frac{15}{8 ( 1 - x ) ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{5}{2 ( 1 - x ) ^{\frac{7}{2}}} \frac{d}{d x} (1 - x)

= - \frac{5}{2 ( 1 - x ) ^{\frac{7}{2}}} \frac{d}{d x} (1 - x)

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

= \frac{3}{4} (- \frac{5}{2 ( 1 - x ) ^{\frac{7}{2}}} (- 1))

Vereinfache

\frac{3}{4} (- \frac{5}{2 ( 1 - x ) ^{\frac{7}{2}}} (- 1)) : \frac{15}{8 ( 1 - x ) ^{\frac{7}{2}}}

= \frac{15}{8 ( 1 - x ) ^{\frac{7}{2}}}

4 x^{2} y^{^{''}} + y = 0

\int \frac{x ^{2}}{6} d x

\frac{d}{d x} (c x cos (2 x))

n = 1 \sum \infty (0.9)^{n}

25 y^{^{''}} - 15 y^{^{'}} - 4 y = 0