derivative of (x^2-1/(x^4-1))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{4} - 1})

- \frac{2 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{4} - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 1 ) ( x ^{4} - 1 ) - \frac{d}{d x} ( x ^{4} - 1 ) ( x ^{2} - 1 )}{( x ^{4} - 1 ) ^{2}}

\frac{d}{d x} (x^{2} - 1) = 2 x

\frac{d}{d x} (x^{4} - 1) = 4 x^{3}

= \frac{2 x ( x ^{4} - 1 ) - 4 x ^{3} ( x ^{2} - 1 )}{( x ^{4} - 1 ) ^{2}}

Vereinfache

\frac{2 x ( x ^{4} - 1 ) - 4 x ^{3} ( x ^{2} - 1 )}{( x ^{4} - 1 ) ^{2}} : - \frac{2 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{2 x}{( x ^{2} + 1 ) ^{2}}

d er i v a t i v e - 0.05 (t + 1.1)^{2.2} + 0.7 t + 0.9

\int z z - 6 d z

\frac{d}{d x} (20 cos (2 x) - 30 sin (2 x))

\int 8 sin (2 x) d x

\frac{d ^{2} x}{d t ^{2}}