What is (\partial)/(\partial y)(yln(y)) ?

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

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(\partial)/(\partial y)(yln(y))

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

ln (y) + 1

Solution steps

\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{\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}

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

Simplify

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

= ln (y) + 1

\int x^{4} + 1 d x

- 9 x^{4} + x^{3}

\int \frac{1}{x ^{3} + 1} d x

\int e^{9 x} cos (2 x) d x

2 t^{2} (\frac{d x}{d t}) = 3 t x + x^{2}

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