What is (\partial)/(\partial y)(e^xxy+e^xy^2+e^xy) ?

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

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(\partial)/(\partial y)(e^xxy+e^xy^2+e^xy)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

\int_{0}^{1} \frac{2 x}{( 2 - x ) ^{2}} d x

\frac{11}{ln ( x )}

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

4 x + 12, x^{2}, 8 - x^{2}

4^{2 x^{2}}

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