What is the derivative of x(sin(x)^2) ?

The derivative of x(sin(x)^2) is sin^2(x)+xsin(2x)

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

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

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

sin^{2} (x) + x sin (2 x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = (sin (x))^{2}

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

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

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

= 1 \cdot (sin (x))^{2} + sin (2 x) x

Simplify

= sin^{2} (x) + x sin (2 x)

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