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^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= - e^{- x} y

\int_{- 2}^{5} - x^{3} + 9 x d x

\frac{d}{d x} (4 cot (x))

f (x) = - 5 e^{- 2.5 x^{2}} x

x \to 0 lim (x^{3} + 2^{2} - x)

x y \frac{d y}{d x} = 1 + y^{2}

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