What is (\partial)/(\partial x)(e^xx+2ye^x) ?

The answer to (\partial)/(\partial x)(e^xx+2ye^x) is e^xx+e^x+2ye^x

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(\partial)/(\partial x)(e^xx+2ye^x)

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

e^{x} x + e^{x} + 2 y e^{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

x \to - 2 lim (x^{3})

d er i v a t i v e \frac{3 + 8 x}{9 - 2 x}

d er i v a t i v e f (t) = (1 t^{2} + 0 t + 0)^{- 8}

\frac{d}{d x} (4^{9^{x^{2}}})

in v erse l a pl a ce \frac{1}{x} \cdot \frac{10}{x ^{2} + x + 10}

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