What is the derivative of 4cos(xsin(x)) ?

The derivative of 4cos(xsin(x)) is 4cos(2x)

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

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

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

4 cos (2 x)

Solution steps

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

Simplify

4 cos (x) sin (x) : 2 sin (2 x)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= 2 cos (2 x) \cdot 2

Simplify

= 4 cos (2 x)

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