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

The answer to (\partial)/(\partial x)(x^2e^x) is 2xe^x+e^xx^2

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

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

2 x e^{x} + e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = e^{x}

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

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

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

= 2 x e^{x} + e^{x} x^{2}

\frac{d}{d x} ((1 - x) ln (1 - x))

\int \frac{3 x ^{2}}{8} d x

\int_{1}^{25} x ln (x) d x

f (x) = \frac{x}{x}

y^{^{'''}} - 4 y^{^{''}} + 4 y^{^{'}} = 8 x

What is (\partial)/(\partial x)(x^2e^x) ?
The answer to (\partial)/(\partial x)(x^2e^x) is 2xe^x+e^xx^2