derivative of (2(x^2-9)/(x^2-4))

Lösung

\frac{d}{d x} (\frac{2 ( x ^{2} - 9 )}{x ^{2} - 4})

\frac{20 x}{( x ^{2} - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 ( x ^{2} - 9 )}{x ^{2} - 4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x ^{2} - 9}{x ^{2} - 4})

Wende die Quotientenregel an:

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

= 2 \cdot \frac{\frac{d}{d x} ( x ^{2} - 9 ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) ( x ^{2} - 9 )}{( x ^{2} - 4 ) ^{2}}

\frac{d}{d x} (x^{2} - 9) = 2 x

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

= 2 \cdot \frac{2 x ( x ^{2} - 4 ) - 2 x ( x ^{2} - 9 )}{( x ^{2} - 4 ) ^{2}}

Vereinfache

2 \cdot \frac{2 x ( x ^{2} - 4 ) - 2 x ( x ^{2} - 9 )}{( x ^{2} - 4 ) ^{2}} : \frac{20 x}{( x ^{2} - 4 ) ^{2}}

= \frac{20 x}{( x ^{2} - 4 ) ^{2}}

n = 0 \sum \infty \frac{n !}{8 ^{n}}

(\frac{sin ( x )}{cos ( x )})^{^{'}}

y^{^{''}} + 6 y^{^{'}} + 11 y = 0

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

im pl i c i t \frac{d y}{d x}, 7 x y + 6 = 0