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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (2 x)

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

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

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

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

Simplify

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

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