What is the derivative of x(ln(x)) ?

The derivative of x(ln(x)) is ln(x)+1

What is the first derivative of x(ln(x)) ?

The first derivative of x(ln(x)) is ln(x)+1

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derivative of

x (ln (x))

ln (x) + 1

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (x)

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

\frac{d x}{d x} = 1

\frac{d}{d 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{\partial}{\partial x} (x + y - 8)

f (x) = (x^{2} + 5) (8 - x)

x \to 1 lim (4 x^{2} + 2)

\frac{4}{x} - 1

\int x e^{\frac{- x ^{2}}{2}} d x

What is the derivative of x(ln(x)) ?
The derivative of x(ln(x)) is ln(x)+1
What is the first derivative of x(ln(x)) ?
The first derivative of x(ln(x)) is ln(x)+1