What is the derivative of 2sin(x-2xcos(x)) ?

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

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

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

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

2 x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= 2 x sin (x)

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