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

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

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

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

2 x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 2 x

Simplify

= 2 x

\int_{0}^{37} x^{2} d x

\frac{3}{4 x + 1}

\frac{d}{d x} (\frac{2 x}{x ^{2} + 1})

\frac{d}{d x} ((x - 4)^{3} e^{- 4 x})

\frac{d y}{d x} = e^{3 x + 5 y}

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