What is the derivative of y=xsin(2x) ?

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

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

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

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derivative of

y = x sin (2 x)

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

Solution steps

\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)

= \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

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

Simplify

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

\int \frac{12}{1 - cos ( 2 x )} d x

\int_{1}^{4} - 7 x ln (x) d x

\int \frac{4 x}{( 3 x ^{2} - 1 ) ^{5}} d x

\int \frac{( 2 x + 3 )}{x ^{2} + 3 x} d x

\int (x^{2} + 1)^{\frac{1}{2}} d x

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