derivative of (4x^2+2x+6/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{4 x ^{2} + 2 x + 6}{x})

\frac{6 x ^{2} + x - 3}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{2} + 2 x + 6}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} + 2 x + 6 ) x - \frac{d}{d x} ( x ) ( 4 x ^{2} + 2 x + 6 )}{( x ) ^{2}}

\frac{d}{d x} (4 x^{2} + 2 x + 6) = 8 x + 2

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

= \frac{( 8 x + 2 ) x - \frac{1}{2 x} ( 4 x ^{2} + 2 x + 6 )}{( x ) ^{2}}

Vereinfache

\frac{( 8 x + 2 ) x - \frac{1}{2 x} ( 4 x ^{2} + 2 x + 6 )}{( x ) ^{2}} : \frac{6 x ^{2} + x - 3}{x x}

= \frac{6 x ^{2} + x - 3}{x x}

\int \frac{( ln ( x ) ) ^{40}}{x} d x

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

d er i v a t i v e f (x) = \frac{2 x}{1 - x}

\int_{4}^{x} \frac{( x - 4 ) ^{2}}{72} d x

x \to 1 lim (\frac{x}{x - 1} - \frac{1}{x})