What is (\partial)/(\partial y)(e^{x+y+1}) ?

The answer to (\partial)/(\partial y)(e^{x+y+1}) is e^{x+y+1}

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(\partial)/(\partial y)(e^{x+y+1})

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

e^{x + y + 1}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= e^{x + y + 1}

\int_{0}^{1} x - x^{2} d x

y = x^{2} + 2 x + 1, y = 2 x + 5

\frac{\partial}{\partial x} (- 6 x y)

\frac{d}{d x} (\frac{1}{5} x^{5} + \frac{1}{12 x ^{3}})

x^{2} y^{^{'}} - 2 x y = sin (4 x) x^{4}

What is (\partial)/(\partial y)(e^{x+y+1}) ?
The answer to (\partial)/(\partial y)(e^{x+y+1}) is e^{x+y+1}