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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int sin^{2} (6 x) cos^{2} (6 x) d x

x^{2}, 12 - x

\frac{d}{d x} (\frac{x ^{3} - y ^{3}}{x - y})

x \to 0 lim (+ (x^{x}))

y^{^{'}} = 7 t y^{2}

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