What is (\partial)/(\partial x)(xe^y+ye^z+ze^x) ?

The answer to (\partial)/(\partial x)(xe^y+ye^z+ze^x) is e^xz+e^y

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(\partial)/(\partial x)(xe^y+ye^z+ze^x)

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

e^{x} z + e^{y}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y e^{z}) = 0

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

= e^{y} + 0 + z e^{x}

Simplify

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

y (1 + x^{2}) y^{^{'}} - x (1 + y^{2}) = 0

y = 12

x \to 0 lim (2 x - 7)

\frac{\partial}{\partial x} (3 - x^{4} + 2 x^{2} - y^{2})

\int_{- \frac{π}{6}}^{0} 2 sec^{3} (x) d x

What is (\partial)/(\partial x)(xe^y+ye^z+ze^x) ?
The answer to (\partial)/(\partial x)(xe^y+ye^z+ze^x) is e^xz+e^y