derivative y=((x-3)^2-4)/(x^2+2)

Lösung

ableitung von

y = \frac{( x - 3 ) ^{2} - 4}{x ^{2} + 2}

\frac{6 x ^{2} - 6 x - 12}{( x ^{2} + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x - 3 ) ^{2} - 4 ) ( x ^{2} + 2 ) - \frac{d}{d x} ( x ^{2} + 2 ) ( ( x - 3 ) ^{2} - 4 )}{( x ^{2} + 2 ) ^{2}}

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

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

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

Vereinfache

\frac{2 ( x - 3 ) ( x ^{2} + 2 ) - 2 x ( ( x - 3 ) ^{2} - 4 )}{( x ^{2} + 2 ) ^{2}} : \frac{6 x ^{2} - 6 x - 12}{( x ^{2} + 2 ) ^{2}}

= \frac{6 x ^{2} - 6 x - 12}{( x ^{2} + 2 ) ^{2}}

d er i v a t i v e \frac{x ^{2} - 5}{1 - 3 x ^{2}}

d er i v a t i v e \frac{2 x}{( x ^{2} + y ^{2} )}

d er i v a t i v e lo g_{10} (x^{6} + 5)

d er i v a t i v e (4 - x^{2})^{2}

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