What is (\partial)/(\partial x)(ye^{x/y}-z) ?

The answer to (\partial)/(\partial x)(ye^{x/y}-z) is e^{x/y}

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(\partial)/(\partial x)(ye^{x/y}-z)

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

e^{\frac{x}{y}}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (z) = 0

= e^{\frac{x}{y}} - 0

Simplify

= e^{\frac{x}{y}}

\frac{d}{d x} (\frac{x ^{2}}{5 + 8 x})

\int \frac{1}{( x - 5 ) ( x - 3 )} d x

3 e^{- 3 t}

\frac{d}{d x} (sin^{2} (x) + 1)

x \to 0 - lim (\frac{8 x ^{4} - 3 x}{x})

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