What is the derivative of xln(2x+1) ?

The derivative of xln(2x+1) is ln(2x+1)+(2x)/(2x+1)

What is the first derivative of xln(2x+1) ?

The first derivative of xln(2x+1) is ln(2x+1)+(2x)/(2x+1)

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\frac{d}{d x} (x ln (2 x + 1))

ln (2 x + 1) + \frac{2 x}{2 x + 1}

Solution steps

\frac{d}{d x} (x ln (2 x + 1))

Apply the Product Rule:

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

f = x, g = ln (2 x + 1)

= \frac{d x}{d x} ln (2 x + 1) + \frac{d}{d x} (ln (2 x + 1)) x

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

\frac{d}{d x} (ln (2 x + 1)) = \frac{2}{2 x + 1}

= 1 \cdot ln (2 x + 1) + \frac{2}{2 x + 1} x

Simplify

1 \cdot ln (2 x + 1) + \frac{2}{2 x + 1} x : ln (2 x + 1) + \frac{2 x}{2 x + 1}

= ln (2 x + 1) + \frac{2 x}{2 x + 1}

What is the derivative of xln(2x+1) ?
The derivative of xln(2x+1) is ln(2x+1)+(2x)/(2x+1)
What is the first derivative of xln(2x+1) ?
The first derivative of xln(2x+1) is ln(2x+1)+(2x)/(2x+1)