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

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

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(\partial)/(\partial x)(xe^y-ye^x)

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

e^{y} - y e^{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y} - y e^{x}

\int_{0}^{1} \frac{3 ^{3 x} - 1}{3 ^{x}} d x

y = (2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}}

\int_{- 1}^{1} x (1 - x)^{2} d x

x \to 0 + lim (\frac{1}{sin ^{2} ( x )})

\frac{d}{d x} (\frac{24 x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}})

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