derivative of (cot^2(2x)/(1+x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

d er i v a t i v e 2 x (x + 5)

\frac{d}{d t} (6 cos^{3} (t))

\int \frac{( 3 x ^{3} - 5 x ^{2} + 10 x - 3 )}{3 x + 1} d x

s im pl i f y \frac{8}{( x ^{3} + x ^{2} + 1 ) ^{3}}

\int t - 1 d t