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

(\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}

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

\int e^{5 x} x d x

\int \frac{2}{x 9 x ^{2} + 1} d x

\int \frac{x ^{2} + 5 x + 7}{x + 3} d x

in v erse l a pl a ce \frac{4 s e ^{- 3 s}}{( s ^{2} + 4 )}

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