derivative of (x^2/(x^2-5))

Lösung

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

- \frac{10 x}{( x ^{2} - 5 ) ^{2}}

Schritte zur Lösung

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

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

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

\frac{d}{d x} (x^{2} - 5) = 2 x

= \frac{2 x ( x ^{2} - 5 ) - 2 x x ^{2}}{( x ^{2} - 5 ) ^{2}}

Vereinfache

\frac{2 x ( x ^{2} - 5 ) - 2 x x ^{2}}{( x ^{2} - 5 ) ^{2}} : - \frac{10 x}{( x ^{2} - 5 ) ^{2}}

= - \frac{10 x}{( x ^{2} - 5 ) ^{2}}

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

d er i v a t i v e 2^{z} lo g_{2} (z)

y^{^{'}} + (\frac{3 y}{( 300 - t )}) = 4

\int \frac{64 x ^{2} - 1}{x} d x

\frac{\partial}{\partial x} (e^{x^{2} y} + x^{2} y)