derivative ((2x+1))/(sqrt(x^3))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

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