What is the derivative of xcos(2x) ?

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

What is the first derivative of xcos(2x) ?

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

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derivative of

x cos (2 x)

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (2 x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot cos (2 x) + (- sin (2 x) \cdot 2) x

Simplify

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

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