What is the first d/(dY)((i)(Li+LY)) ?

The first d/(dY)((i)(Li+LY)) is iL

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d/(dY)((i)(Li+LY))

\frac{d}{d Y} ((i) (L i + L Y))

i L

Solution steps

\frac{d}{d Y} ((i) (L i + L Y))

Simplify

(i) (L i + L Y) : - L + i L Y

= \frac{d}{d Y} (- L + i L Y)

Apply the Sum/Difference Rule:

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

= - \frac{d L}{d Y} + \frac{d}{d Y} (i L Y)

\frac{d L}{d Y} = 0

\frac{d}{d Y} (i L Y) = i L

= - 0 + i L

Simplify

= i L

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