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

Lösung

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

\int 3 x (2 - 3 x^{2}) d x

\int x^{2} cos (9 x) d x

\frac{\partial}{\partial x} (x yz e^{x^{2} + y^{2} + z^{2}})

\int x 4 a^{2} - x^{2} d x

\frac{\partial}{\partial y} (x^{2} + y^{2} + z^{2} + x y)