What is (\partial)/(\partial y)((yln(y))/(x-1)) ?

The answer to (\partial)/(\partial y)((yln(y))/(x-1)) is (ln(y)+1)/(x-1)

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(\partial)/(\partial y)((yln(y))/(x-1))

\frac{\partial}{\partial y} (\frac{y ln ( y )}{x - 1})

\frac{ln ( y ) + 1}{x - 1}

Solution steps

\frac{\partial}{\partial y} (\frac{y ln ( y )}{x - 1})

Treat

x

as a constant

Take the constant out:

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

= \frac{1}{x - 1} \frac{\partial}{\partial y} (y ln (y))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = ln (y)

= \frac{1}{x - 1} (\frac{\partial}{\partial y} (y) ln (y) + \frac{\partial}{\partial y} (ln (y)) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (ln (y)) = \frac{1}{y}

= \frac{1}{x - 1} (1 \cdot ln (y) + \frac{1}{y} y)

Simplify

\frac{1}{x - 1} (1 \cdot ln (y) + \frac{1}{y} y) : \frac{ln ( y ) + 1}{x - 1}

= \frac{ln ( y ) + 1}{x - 1}

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What is (\partial)/(\partial y)((yln(y))/(x-1)) ?
The answer to (\partial)/(\partial y)((yln(y))/(x-1)) is (ln(y)+1)/(x-1)