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

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

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

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

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

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

Simplify

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

\int c x^{2} d x

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{2}})

\int \frac{x ^{2} - 2}{x - 1} d x

\frac{d x}{d t} = k + x r

f (x) = x^{2} cos^{4} (x)

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