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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

n = 0 \sum \infty - 6 (\frac{1}{4})^{2 n}

\int_{0}^{1} \frac{2 x}{( x ^{2} + 3 ) ^{3}} d x

x \to \infty lim \frac{( e ^{x^{4} - x^{2}} )}{2}

d er i v a t i v e f (x) = x 1 + x^{2}

\int \frac{e ^{- 2 x}}{1 + e ^{- x}} d x