derivative (7x^2+5sqrt(x))/(4x)

Lösung

ableitung von

\frac{7 x ^{2} + 5 x}{4 x}

\frac{14 x ^{2} - 5 x}{8 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x ^{2} + 5 x}{4 x})

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (\frac{7 x ^{2} + 5 x}{x})

Wende die Quotientenregel an:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 7 x ^{2} + 5 x ) x - \frac{d x}{d x} ( 7 x ^{2} + 5 x )}{x ^{2}}

\frac{d}{d x} (7 x^{2} + 5 x) = 14 x + \frac{5}{2 x}

\frac{d x}{d x} = 1

= \frac{1}{4} \cdot \frac{( 14 x + \frac{5}{2 x} ) x - 1 \cdot ( 7 x ^{2} + 5 x )}{x ^{2}}

Vereinfache

\frac{1}{4} \cdot \frac{( 14 x + \frac{5}{2 x} ) x - 1 \cdot ( 7 x ^{2} + 5 x )}{x ^{2}} : \frac{14 x ^{2} - 5 x}{8 x ^{2}}

= \frac{14 x ^{2} - 5 x}{8 x ^{2}}

\int \frac{lo g _{9} ( x )}{x} d x

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d er i v a t i v e (5 - 5 x^{3})^{3} + \frac{1}{5 - 5 x ^{3}}