What is (\partial)/(\partial z)(xe^{-z}) ?

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

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(\partial)/(\partial z)(xe^{-z})

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

- e^{- z} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - e^{- z} x

\frac{\partial}{\partial z} (x sin (y - z))

x \to 0 lim (5 e)

\frac{d}{d x} (\frac{9}{x + 7})

\frac{\partial}{\partial x} (sin (α) cos (β))

\frac{d}{d x} (24 e^{- 3 x})

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