derivative of (4x+9/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{4 x + 9}{x})

\frac{4 x - 9}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x + 9}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x + 9 ) x - \frac{d}{d x} ( x ) ( 4 x + 9 )}{( x ) ^{2}}

\frac{d}{d x} (4 x + 9) = 4

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

= \frac{4 x - \frac{1}{2 x} ( 4 x + 9 )}{( x ) ^{2}}

Vereinfache

\frac{4 x - \frac{1}{2 x} ( 4 x + 9 )}{( x ) ^{2}} : \frac{4 x - 9}{2 x x}

= \frac{4 x - 9}{2 x x}

\int \frac{x - 1}{x + 1} d x

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\frac{d ^{2} y}{d t ^{2}} + 9 y = 0

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