What is (\partial)/(\partial x)(-4e^{-x-y}) ?

The answer to (\partial)/(\partial x)(-4e^{-x-y}) is 4e^{-x-y}

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(\partial)/(\partial x)(-4e^{-x-y})

\frac{\partial}{\partial x} (- 4 e^{- x - y})

4 e^{- x - y}

Solution steps

\frac{\partial}{\partial x} (- 4 e^{- x - y})

Treat

y

as a constant

Take the constant out:

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

= - 4 \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

= - 4 e^{- x - y} (- 1)

Simplify

= 4 e^{- x - y}

3 \frac{d y}{d x} + 12 y = 4

x \to 3 lim (\frac{x}{x - 2})

\frac{\partial}{\partial y} (y^{\frac{2}{3}})

\frac{d}{d x} (ln (6 x^{2}))

t y^{^{'}} + 3 y = 0

What is (\partial)/(\partial x)(-4e^{-x-y}) ?
The answer to (\partial)/(\partial x)(-4e^{-x-y}) is 4e^{-x-y}