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

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

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(\partial)/(\partial x)(x^2+xe^{2y}-y)

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

2 x + e^{2 y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

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

= 2 x + e^{2 y} - 0

Simplify

= 2 x + e^{2 y}

\frac{d x}{d y} = 4 (x^{2} + 1)

x \to \infty lim (\frac{4 x ^{3} + 8}{4 x ^{3} + 64 x ^{6} + 3})

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

\frac{arcsin ( 3 x )}{x}

x \to 1 lim (2 x + 2)

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