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

\frac{d}{d x} (e^{2 x} - x^{2} - 1)

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\int csc (- 4 x) d x

\int \frac{( ln ^{2} ( x ) )}{x ^{2}} d x

\int_{1}^{3} \frac{x}{x ^{2} + 6 x + 13} d 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