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}}

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\frac{d}{d x} (3 x^{2} 5 x + 3)

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\frac{d}{d x} (3 sin (x))

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