What is (\partial)/(\partial x)(xsin(2x)) ?

The answer to (\partial)/(\partial x)(xsin(2x)) is sin(2x)+2xcos(2x)

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(\partial)/(\partial x)(xsin(2x))

\frac{\partial}{\partial x} (x sin (2 x))

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

Solution steps

\frac{\partial}{\partial x} (x sin (2 x))

Apply the Product Rule:

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

f = x, g = sin (2 x)

= \frac{\partial}{\partial x} (x) sin (2 x) + \frac{\partial}{\partial x} (sin (2 x)) x

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

What is (\partial)/(\partial x)(xsin(2x)) ?
The answer to (\partial)/(\partial x)(xsin(2x)) is sin(2x)+2xcos(2x)