What is the first d/(dy)(e^{-y}) ?

The first d/(dy)(e^{-y}) is -e^{-y}

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d/(dy)(e^{-y})

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

- e^{- y}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{- y} (- 1)

Simplify

= - e^{- y}

x^{\frac{1}{2}}

y = 5 e^{(6 x + 7)}

\int e^{- x} (1 + e^{- x})^{3} d x

\frac{d}{d x} (0.01 x^{2})

f (x) = 2 - x^{2}