derivative of x/(1+4x^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

1 \cdot (1 + 4 x^{2}) - 8 xx = 1 - 4 x^{2}

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

\int \frac{k}{x} d x

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

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

d er i v a t i v e e^{\frac{- x ^{2}}{2}}

\int_{0}^{1} - \frac{6 y}{e ^{2 y}} d y