What is (\partial)/(\partial x)(xln(x)) ?

The answer to (\partial)/(\partial x)(xln(x)) is ln(x)+1

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(\partial)/(\partial x)(xln(x))

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

ln (x) + 1

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (x)

= \frac{\partial}{\partial x} (x) ln (x) + \frac{\partial}{\partial x} (ln (x)) x

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

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

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

Simplify

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

= ln (x) + 1

\frac{d}{d x} (2 x + \frac{200}{x})

f (x) = \frac{32}{0}

\frac{d}{d x} (ln^{2} (x) + 2 ln (x))

\int \frac{1}{x ^{2} ( x ^{2} - 16 )} d x

\int ln (cos (x)) tan (x) d x

What is (\partial)/(\partial x)(xln(x)) ?
The answer to (\partial)/(\partial x)(xln(x)) is ln(x)+1