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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

\frac{1}{x} x^{2} = x^{\frac{3}{2}}

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

\frac{d}{d y} (x^{2} - y^{2})

n = 1 \sum \infty \frac{n}{n ^{3} + 2}

n = 0 \sum \infty \frac{1}{2 ^{n + 2}}

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

\frac{d y}{d x} = - \frac{2}{x}