What is (\partial)/(\partial x)(4y+xe^{x/y}) ?

The answer to (\partial)/(\partial x)(4y+xe^{x/y}) is e^{x/y}+(e^{x/y}x)/y

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(\partial)/(\partial x)(4y+xe^{x/y})

\frac{\partial}{\partial x} (4 y + x e^{\frac{x}{y}})

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

Solution steps

\frac{\partial}{\partial x} (4 y + x e^{\frac{x}{y}})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 y) + \frac{\partial}{\partial x} (x e^{\frac{x}{y}})

\frac{\partial}{\partial x} (4 y) = 0

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

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

Simplify

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

y^{^{''}} - 4 y^{^{'}} + 5 y = 3 e^{2 t} sin (t)

- \frac{4 x}{x ^{2} + 1}

\int 7 sec^{2} (x) d x

\frac{d}{d x} (2 x^{2} - 1 + c e^{- 2 x^{2}})

\frac{\partial}{\partial x} (x yz + x^{3} + y^{4} + z^{5})

What is (\partial)/(\partial x)(4y+xe^{x/y}) ?
The answer to (\partial)/(\partial x)(4y+xe^{x/y}) is e^{x/y}+(e^{x/y}x)/y