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

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

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

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

e^{- x - y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= e^{- x - y}

\int_{\frac{1}{2}}^{1} (x^{- 3} - 24) d x

y^{^{''}} + 2 y^{^{'}} + y = 2

x \to 0 lim (x \cdot e^{x})

\frac{d}{d x} (\frac{10 lo g _{4} ( x )}{x})

x \to \infty lim (\frac{6 ^{x + 1}}{7 ^{x - 1}})

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