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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

\frac{d y}{d x} + x^{2} y = 1

x \to 0 lim (8^{- x})

3 ln (x) - \frac{x ^{2}}{24}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{x} + e^{2 x} + e^{- x}

\frac{x ^{2}}{1 + 2 x}

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