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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

= y e^{\frac{x}{y}} \frac{1}{y}

Simplify

y e^{\frac{x}{y}} \frac{1}{y} : e^{\frac{x}{y}}

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

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

e^{- 2 s} (\frac{1}{s + 1})

\int t e^{- 2 t} d t

\frac{\partial}{\partial x} (50 x - 0.5 x^{2} + 75 y - y^{2})

\frac{\partial}{\partial x} (- ln (x^{2} + 1))

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