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

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

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

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

e^{x}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + e^{x}

Simplify

= e^{x}

\frac{d}{d x} (- 4 x^{3} + 10 x^{2} - x)

\frac{\partial}{\partial x} (\frac{2 x}{3 y})

\int arctan (x) x d x

x \to 3 - lim (7 - x)

f (x) = ln (x^{2} - 3 x + 1), at x = 3

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