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

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

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

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

- e^{- y}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{- y} (- 1)

Simplify

= - e^{- y}

x \to 1 lim (2 x - 2)

y = \frac{3}{x}

\int \frac{1}{( x ^{2} + 16 ) ^{3}} d x

\int \frac{1}{3 x ^{2} + 12} d x

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