What is the derivative of xcos(4x) ?

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

What is the first derivative of xcos(4x) ?

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

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\frac{d}{d x} (x cos (4 x))

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

Solution steps

\frac{d}{d x} (x cos (4 x))

Apply the Product Rule:

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

f = x, g = cos (4 x)

= \frac{d x}{d x} cos (4 x) + \frac{d}{d x} (cos (4 x)) x

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= 1 \cdot cos (4 x) + (- sin (4 x) \cdot 4) x

Simplify

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

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