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)})

Simplify

e^{- (x + y)} : e^{- x - y}

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

Treat

y

as a constant

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}

(t^{2} - 1) y^{^{'}} + 2 t y^{2} = 0

\int \frac{t ^{2}}{( a + b t ^{3} ) ^{2}} d t

x y^{^{'}} = 2 x^{2} y + 3 x^{3} e^{x^{2}}

\int_{4}^{9} \frac{1}{5 - x} d x

\int x^{2} x - 5 d x

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