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

Lösung

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

\frac{2 x ^{5} - 4 x ^{3} - 2 x}{( x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

4 x^{3} (x^{2} - 1) - 2 x (x^{4} + 1) : 2 x^{5} - 4 x^{3} - 2 x

= \frac{2 x ^{5} - 4 x ^{3} - 2 x}{( x ^{2} - 1 ) ^{2}}

a re a \frac{3}{x}, 12 x, \frac{1}{12} x

\frac{d}{d x} (x^{3} (1 - x)^{100} + x^{4} - 5 π)

y^{^{'}} + 7 y = 0

x \to 5 lim (\frac{5}{( x - 2 ) ^{2}})

(x^{2} + x y + y^{2}) d x = (x^{2} + x y) d y