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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int \frac{1 + x}{1 - x} d x

\frac{\partial}{\partial y} (ln (2 x + y + 1))

\int - 4 e^{- \frac{x}{4}} d x

(x, y) \to (2, 1) lim (\frac{x - 2 y}{x ^{3} - 8 y ^{3}})

\frac{\partial}{\partial y} (y^{4} sin (6 x))

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