derivative of (1-cos(2x)/(1+cos(2x)))

Lösung

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

2 tan (x) sec^{2} (x)

Schritte zur Lösung

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

Vereinfache

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

= \frac{d}{d x} (tan^{2} (x))

Wende die Kettenregel an:

2 tan (x) \frac{d}{d x} (tan (x))

= 2 tan (x) \frac{d}{d x} (tan (x))

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= 2 tan (x) sec^{2} (x)

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

\frac{d}{d x} (4 e^{- 6 x^{2}})

\int \frac{5 ( 1 - tan ^{2} ( x ) )}{sec ^{2} ( x )} d x

d er i v a t i v e x - 4

\int \frac{25 x ^{2} + 4}{x ^{4}} d x