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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx

Simplify

1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx : e^{x^{2}} + 2 e^{x^{2}} x^{2}

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

x y^{^{'}} - x^{2} y = - x^{2}

x^{2} - 3 x + 2

\int_{- 4}^{0} 2 + 16 - x^{2} d x

\int_{- 1}^{2} x - x^{2} + 2 d x

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

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