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

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

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

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

2 x + e^{2 y}

Solution steps

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

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

= 2 x + e^{2 y}

\frac{d}{d x} (\frac{2 arctan ( x )}{1 + x ^{2}})

x = 0, y = x^{2}, y = x + 2

x \to - 1 lim (- 6)

9 x - (sin^{2} (2 x))

\frac{\partial}{\partial x} (x sin (y))

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