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Beliebt Rechnen >

derivative of (6x-x^2^{1/2})

Lösung

\frac{d}{d x} ((6 x - x^{2})^{\frac{1}{2}})

Lösung

\frac{3 - x}{( 6 x - x ^{2} ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((6 x - x^{2})^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x - x^{2})

= \frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x - x^{2})

\frac{d}{d x} (6 x - x^{2}) = 6 - 2 x

= \frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} (6 - 2 x)

Vereinfache

\frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} (6 - 2 x) : \frac{3 - x}{( 6 x - x ^{2} ) ^{\frac{1}{2}}}

= \frac{3 - x}{( 6 x - x ^{2} ) ^{\frac{1}{2}}}

Graph

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