What is (\partial)/(\partial x)(2y+xe^y) ?

The answer to (\partial)/(\partial x)(2y+xe^y) is e^y

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(\partial)/(\partial x)(2y+xe^y)

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

e^{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 y) = 0

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

= 0 + e^{y}

Simplify

= e^{y}

\frac{d y}{d t} = 0.06 y - 4000

5 x^{2} + 2 x - 3

y^{^{'}} = \frac{x ^{2} \cdot e ^{(\frac{y}{x})} + y ^{2}}{x \cdot y}

x \to 2 lim (x^{2} - 4 x + 4)

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (1) = 0, y^{^{'}} (1) = 1

What is (\partial)/(\partial x)(2y+xe^y) ?
The answer to (\partial)/(\partial x)(2y+xe^y) is e^y