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

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

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

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

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

Solution steps

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

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 e^{x} y)

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

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

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

\int_{2}^{3} 3 - x d x

\frac{d}{d x} (ln (x) csc (x))

y^{^{'}} = - 5 sin (3 t) + 2 cos (4 t)

x \to 0 lim (\frac{1}{sin ( 5 x )})

y = - x^{2} + 16, x = - 2, y = 0, x = 3

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