What is the first d/(dy)(yln(x)) ?

The first d/(dy)(yln(x)) is ln(x)

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d/(dy)(yln(x))

\frac{d}{d y} (y ln (x))

ln (x)

Solution steps

\frac{d}{d y} (y ln (x))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (x) \frac{d y}{d y}

Apply the common derivative:

\frac{d y}{d y} = 1

= ln (x) \cdot 1

Simplify

= ln (x)