derivative of 5/(xsqrt(x))

Lösung

\frac{d}{d x} (\frac{5}{x x})

- \frac{15}{2 x ^{\frac{5}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{x x})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{1}{x x})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

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

Vereinfache

5 (- \frac{1}{( x x ) ^{2}} \cdot \frac{3 x}{2}) : - \frac{15}{2 x ^{\frac{5}{2}}}

= - \frac{15}{2 x ^{\frac{5}{2}}}

s l o p e in t erce pt (z, 2), (- 2, - 6)

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x^{2} y^{^{''}} + x y^{^{'}} + 25 y = 0

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