What is (\partial)/(\partial y)(e^{x+y+3}) ?

The answer to (\partial)/(\partial y)(e^{x+y+3}) is e^{x+y+3}

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(\partial)/(\partial y)(e^{x+y+3})

\frac{\partial}{\partial y} (e^{x + y + 3})

e^{x + y + 3}

Solution steps

\frac{\partial}{\partial y} (e^{x + y + 3})

Treat

x

as a constant

Apply the chain rule:

e^{x + y + 3} \frac{\partial}{\partial y} (x + y + 3)

= e^{x + y + 3} \frac{\partial}{\partial y} (x + y + 3)

\frac{\partial}{\partial y} (x + y + 3) = 1

= e^{x + y + 3} \cdot 1

Simplify

= e^{x + y + 3}

\frac{\partial}{\partial x} (\frac{3}{x} - 1 - y)

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x \to 3 lim (\frac{x}{x ^{2} - 9})

\frac{\partial}{\partial x} (5 x y - 10 y)

\frac{d}{d x} ((8 x - 2 x^{2}) cos (y))

What is (\partial)/(\partial y)(e^{x+y+3}) ?
The answer to (\partial)/(\partial y)(e^{x+y+3}) is e^{x+y+3}