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

解

\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)

解答ステップ

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

積の法則を適用:

(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)

簡素化

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