What is (\partial)/(\partial x)(3-(e^y)/(e^{x+1)}) ?

The answer to (\partial)/(\partial x)(3-(e^y)/(e^{x+1)}) is e^{y-x-1}

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(\partial)/(\partial x)(3-(e^y)/(e^{x+1)})

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

e^{y - x - 1}

Solution steps

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

Simplify

3 - \frac{e ^{y}}{e ^{x + 1}} : 3 - e^{y - x - 1}

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3) = 0

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

= 0 - (- e^{y - x - 1})

Simplify

= e^{y - x - 1}

What is (\partial)/(\partial x)(3-(e^y)/(e^{x+1)}) ?
The answer to (\partial)/(\partial x)(3-(e^y)/(e^{x+1)}) is e^{y-x-1}