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

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

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

\frac{\partial}{\partial x} (y \cdot 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}}

x \to 0 lim (\frac{sin ( 2 x ) sin ( 3 x )}{sin ( 2 x ) sin ( 3 x )})

\frac{d x}{d t} - 5 x = sin (2 t)

\frac{\partial}{\partial x} (\frac{7 y}{x ^{2} + 7 y ^{2}})

x \to 1 lim (\frac{3}{x} - \frac{2}{ln ( x )})

e^{j (2 t + 4)}

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