What is (\partial)/(\partial z)(ye^x+xln(z)) ?

The answer to (\partial)/(\partial z)(ye^x+xln(z)) is x/z

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(\partial)/(\partial z)(ye^x+xln(z))

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

\frac{x}{z}

Solution steps

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

Treat

y, x

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial z} (x ln (z)) = \frac{x}{z}

= 0 + \frac{x}{z}

Simplify

= \frac{x}{z}

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

\int \frac{1}{1 + 2 x} d x

x \to 0 lim (\frac{( 2 + x ) ^{2} - 4}{h ( x )})

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

\frac{\partial}{\partial h ( w )} (\frac{w}{h ( w ) ^{2}})

What is (\partial)/(\partial z)(ye^x+xln(z)) ?
The answer to (\partial)/(\partial z)(ye^x+xln(z)) is x/z