What is the first d/(dy)(1-e^y) ?

The first d/(dy)(1-e^y) is -e^y

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d/(dy)(1-e^y)

\frac{d}{d y} (1 - e^{y})

- e^{y}

Solution steps

\frac{d}{d y} (1 - e^{y})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d y} (1) = 0

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

= 0 - e^{y}

Simplify

= - e^{y}