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

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

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

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

e^{x^{2} + y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{x^{2} + y} \cdot 1

Simplify

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

\frac{d y}{d t} = 8 y, y (4) = 4

\frac{1}{2 s}

f (x) = cos (\frac{1}{x})

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

(3^{2} + 5 x)^{4} (2 x - 2)^{3}

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