What is the derivative of xln(2x+3) ?

The derivative of xln(2x+3) is ln(2x+3)+(2x)/(2x+3)

What is the first derivative of xln(2x+3) ?

The first derivative of xln(2x+3) is ln(2x+3)+(2x)/(2x+3)

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\frac{d}{d x} (x ln (2 x + 3))

ln (2 x + 3) + \frac{2 x}{2 x + 3}

Solution steps

\frac{d}{d x} (x ln (2 x + 3))

Apply the Product Rule:

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

f = x, g = ln (2 x + 3)

= \frac{d x}{d x} ln (2 x + 3) + \frac{d}{d x} (ln (2 x + 3)) x

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

\frac{d}{d x} (ln (2 x + 3)) = \frac{2}{2 x + 3}

= 1 \cdot ln (2 x + 3) + \frac{2}{2 x + 3} x

Simplify

1 \cdot ln (2 x + 3) + \frac{2}{2 x + 3} x : ln (2 x + 3) + \frac{2 x}{2 x + 3}

= ln (2 x + 3) + \frac{2 x}{2 x + 3}

x y^{^{'}} = y + 2 x y

(1 + x)^{2}

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

arctan (16 x)

What is the derivative of xln(2x+3) ?
The derivative of xln(2x+3) is ln(2x+3)+(2x)/(2x+3)
What is the first derivative of xln(2x+3) ?
The first derivative of xln(2x+3) is ln(2x+3)+(2x)/(2x+3)