What is the derivative of xln|x| ?

The derivative of xln|x| is ln|x|+1

What is the first derivative of xln|x| ?

The first derivative of xln|x| is ln|x|+1

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\frac{d}{d x} (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 e^{2 y})

y^{^{''}} - 5 y^{^{'}} = 0

\frac{d}{d x} (\frac{sin ( 2 x )}{1 + cos ( 2 x )})

3 x^{2} - 14 x + 5

\frac{9}{x ^{2} + 2}

What is the derivative of xln|x| ?
The derivative of xln|x| is ln|x|+1
What is the first derivative of xln|x| ?
The first derivative of xln|x| is ln|x|+1