What is (\partial)/(\partial x)(x*ln(x)) ?

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

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(\partial)/(\partial x)(x*ln(x))

\frac{\partial}{\partial x} (x \cdot 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

\int 2 π y (8 - y^{\frac{3}{2}}) d y

f (x) = (ln (x))^{3}, at x = 11

f (x) = x^{3} + 2 x, at x = 1

\frac{d}{d x} (\frac{x ^{3} + 3 x + 2}{x ^{2} - 1})

x^{2} y^{^{''}} - 5 x y^{^{'}} + 13 y = 0

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