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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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