What is (\partial)/(\partial z)(3ye^{-z}) ?

The answer to (\partial)/(\partial z)(3ye^{-z}) is -3e^{-z}y

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(\partial)/(\partial z)(3ye^{-z})

\frac{\partial}{\partial z} (3 y e^{- z})

- 3 e^{- z} y

Solution steps

\frac{\partial}{\partial z} (3 y e^{- z})

Treat

y

as a constant

Take the constant out:

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

= 3 y \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

= 3 y e^{- z} (- 1)

Simplify

= - 3 e^{- z} y

\frac{d y}{d x} = (\frac{( 2 y + 3 )}{4 x + 5})^{2}

\frac{d}{d x} (ln (\frac{3 x + 1}{x ^{2} - 2}))

3 x e^{x} csc (x)

x \to 0 lim (sin^{2} (x) (\frac{1}{x}))

x \to - 1 lim (\frac{1}{x ^{2} + 1})

What is (\partial)/(\partial z)(3ye^{-z}) ?
The answer to (\partial)/(\partial z)(3ye^{-z}) is -3e^{-z}y