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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

\int ln (x) x^{13} d x

\int_{1}^{4} \frac{5}{x ^{2}} d x

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

\frac{d}{d x} (\frac{1}{4 x + 4})

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