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}}

\int \frac{1}{( 9 x ^{2} - 1 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (\frac{1 - 4 x}{6 + x})

\int \frac{1}{( u ^{2} + 9 ) ^{\frac{5}{2}}} d u

\frac{d}{d x} (x^{2} lo g_{10} (x))

\frac{d}{d x} (7 tan (x))