derivative of cos(2x-1tan(1-2x))

Lösung

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

- 2 sin (2 x - 1) tan (1 - 2 x) - 2 sec^{2} (1 - 2 x) cos (2 x - 1)

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (2 x - 1), g = tan (1 - 2 x)

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

\frac{d}{d x} (cos (2 x - 1)) = - sin (2 x - 1) \cdot 2

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

= (- sin (2 x - 1) \cdot 2) tan (1 - 2 x) + (- 2 sec^{2} (1 - 2 x)) cos (2 x - 1)

Vereinfache

= - 2 sin (2 x - 1) tan (1 - 2 x) - 2 sec^{2} (1 - 2 x) cos (2 x - 1)

a re a e^{x}, x e^{x^{2}}, [0, 1]

d er i v a t i v e f (x) = \frac{1}{( 3 - x ) ^{2}}

x \to 0 - lim (3 x)

d er i v a t i v e 4 t^{\frac{- 3}{8}}

\frac{d}{d x} (\frac{π}{6})