What is the derivative of cos(2x-1*tan(1-2x)) ?

The derivative of cos(2x-1*tan(1-2x)) is -2sin(2x-1)tan(1-2x)-2sec^2(1-2x)cos(2x-1)

What is the first derivative of cos(2x-1*tan(1-2x)) ?

The first derivative of cos(2x-1*tan(1-2x)) is -2sin(2x-1)tan(1-2x)-2sec^2(1-2x)cos(2x-1)

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\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)

Solution steps

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

Apply the Product Rule:

(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)

Simplify

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

What is the derivative of cos(2x-1*tan(1-2x)) ?
The derivative of cos(2x-1*tan(1-2x)) is -2sin(2x-1)tan(1-2x)-2sec^2(1-2x)cos(2x-1)
What is the first derivative of cos(2x-1*tan(1-2x)) ?
The first derivative of cos(2x-1*tan(1-2x)) is -2sin(2x-1)tan(1-2x)-2sec^2(1-2x)cos(2x-1)