What is (\partial)/(\partial x)(7e^{x/y}) ?

The answer to (\partial)/(\partial x)(7e^{x/y}) is (7e^{x/y})/y

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(\partial)/(\partial x)(7e^{x/y})

\frac{\partial}{\partial x} (7 e^{\frac{x}{y}})

\frac{7 e ^{\frac{x}{y}}}{y}

Solution steps

\frac{\partial}{\partial x} (7 e^{\frac{x}{y}})

Treat

y

as a constant

Take the constant out:

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

= 7 \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}

= 7 e^{\frac{x}{y}} \frac{1}{y}

Simplify

7 e^{\frac{x}{y}} \frac{1}{y} : \frac{7 e ^{\frac{x}{y}}}{y}

= \frac{7 e ^{\frac{x}{y}}}{y}

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What is (\partial)/(\partial x)(7e^{x/y}) ?
The answer to (\partial)/(\partial x)(7e^{x/y}) is (7e^{x/y})/y