What is the derivative of cos(2x)-2xsin(2x) ?

The derivative of cos(2x)-2xsin(2x) is -4sin(2x)-4xcos(2x)

What is the first derivative of cos(2x)-2xsin(2x) ?

The first derivative of cos(2x)-2xsin(2x) is -4sin(2x)-4xcos(2x)

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derivative of

cos (2 x) - 2 x sin (2 x)

- 4 sin (2 x) - 4 x cos (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2 x sin (2 x)) = 2 (sin (2 x) + 2 x cos (2 x))

= - sin (2 x) \cdot 2 - 2 (sin (2 x) + 2 x cos (2 x))

Simplify

- sin (2 x) \cdot 2 - 2 (sin (2 x) + 2 x cos (2 x)) : - 4 sin (2 x) - 4 x cos (2 x)

= - 4 sin (2 x) - 4 x cos (2 x)

What is the derivative of cos(2x)-2xsin(2x) ?
The derivative of cos(2x)-2xsin(2x) is -4sin(2x)-4xcos(2x)
What is the first derivative of cos(2x)-2xsin(2x) ?
The first derivative of cos(2x)-2xsin(2x) is -4sin(2x)-4xcos(2x)