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

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

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

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

2 x - e^{x + y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 x + 0 - e^{x + y}

Simplify

= 2 x - e^{x + y}

\int \frac{( y - 2 ) ^{2}}{y} d y

- 5 t^{4}

y = arctanh (\frac{1}{x})

\frac{d}{d x} (\frac{t}{x})

y = (2 x - 5)^{\frac{1}{3}}

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