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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (x^{- 6 c o s (x)})

\frac{\partial}{\partial x} (sin (x - y) + (x - y))

\int e^{\frac{x}{l}} d x

\int (x^{\frac{4}{3}} - 3 x^{\frac{5}{2}}) d x

\int_{0}^{2 π} sin^{2} (x co) s^{2} x