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

n \to \infty lim (n^{4} + 2 n^{3} - (n^{2} + n))

\frac{8 x}{e ^{x}}

\int_{0}^{5} 5 x - 1 d x

\int_{0}^{1} (9 x^{e} + 2 e^{x}) d x

\frac{d y}{d x} = 2 x y^{2} + 3 x^{2} y^{2}

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