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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

x \to 0 lim (\frac{2}{x} - \frac{2}{x})

\frac{2}{x}, \frac{2}{x ^{2}}, x = 4

f (x) = 6 sec (x) - 5 x

\frac{d}{d x} (sec (5) x^{2})

n = 1 \sum \infty \frac{7}{n ^{5}}

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