derivative of (7sqrt(x)/(2x^3))

Lösung

\frac{d}{d x} (\frac{7 x}{2 x ^{3}})

- \frac{35}{4 x ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x}{2 x ^{3}})

Entferne die Konstante:

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

= \frac{7}{2} \frac{d}{d x} (\frac{x}{x ^{3}})

Wende die Quotientenregel an:

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

= \frac{7}{2} \cdot \frac{\frac{d}{d x} ( x ) x ^{3} - \frac{d}{d x} ( x ^{3} ) x}{( x ^{3} ) ^{2}}

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

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

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

Vereinfache

\frac{7}{2} \cdot \frac{\frac{1}{2 x} x ^{3} - 3 x ^{2} x}{( x ^{3} ) ^{2}} : - \frac{35}{4 x ^{\frac{7}{2}}}

= - \frac{35}{4 x ^{\frac{7}{2}}}

f (x) = 1 - 3 x^{2}

\int (2 x + 5)^{2} d x

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