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

Lösung

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

\frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} - 1)^{4}) = 8 x (x^{2} - 1)^{3}

= \frac{1 \cdot ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x}{( ( x ^{2} - 1 ) ^{4} ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x}{( ( x ^{2} - 1 ) ^{4} ) ^{2}} : \frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

= \frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

\int tan^{2} (x) \cdot sec (x) d x

\frac{d}{d x} (ln (ln (12 x)))

\int \frac{1}{2 sin ^{2} ( x ) + 3 cos ^{2} ( x )} d x

y^{^{''}} + 81 y = cos (2 t)

d er i v a t i v e y = \frac{2}{x ^{3}}