What is the first d/(dX)(XY+YZ(Y+Z)) ?

The first d/(dX)(XY+YZ(Y+Z)) is Y

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d/(dX)(XY+YZ(Y+Z))

\frac{d}{d X} (X Y + Y Z (Y + Z))

Y

Solution steps

\frac{d}{d X} (X Y + Y Z (Y + Z))

Treat

Y, Z

as constants

Apply the Sum/Difference Rule:

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

= \frac{d}{d X} (X Y) + \frac{d}{d X} (Y Z (Y + Z))

\frac{d}{d X} (X Y) = Y

\frac{d}{d X} (Y Z (Y + Z)) = 0

= Y + 0

Simplify

= Y

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