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

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

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

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

2 y

Solution steps

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

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} (y^{2})

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

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

= 0 + 2 y

Simplify

= 2 y

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

\frac{d}{d x} (\frac{1}{x - 1} + \frac{1}{x + 1})

\int \frac{1}{x - 5} d x

\frac{d}{d x} (x + π)

y = \frac{1}{x ^{9}}

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