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

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

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

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

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

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

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

Simplify

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

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