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

The answer to (\partial)/(\partial x)(x^2e^{x^2}) is 2e^{x^2}x+2e^{x^2}x^3

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

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

2 e^{x^{2}} x + 2 e^{x^{2}} x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

e^{x^{2}} \cdot 2 x x^{2} = 2 e^{x^{2}} x^{3}

= 2 e^{x^{2}} x + 2 e^{x^{2}} x^{3}

\frac{\partial}{\partial x} (e^{x} sin (x y))

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\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

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What is (\partial)/(\partial x)(x^2e^{x^2}) ?
The answer to (\partial)/(\partial x)(x^2e^{x^2}) is 2e^{x^2}x+2e^{x^2}x^3