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

The answer to (\partial)/(\partial y)(x^2+y-e^{x+y}) is -e^{x+y}+1

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

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

- e^{x + y} + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 + 1 - e^{x + y}

Simplify

= - e^{x + y} + 1

\int \frac{x}{e ^{x}} d x

\int 2 x \cdot sec^{2} (3 x) d x

x \to 0 lim (e^{2 π})

\int e^{x} x d x

\frac{1}{( s - 3 ) ^{2} + 3}

What is (\partial)/(\partial y)(x^2+y-e^{x+y}) ?
The answer to (\partial)/(\partial y)(x^2+y-e^{x+y}) is -e^{x+y}+1