What is the derivative of 4xln(2x+1) ?

The derivative of 4xln(2x+1) is 4(ln(2x+1)+(2x)/(2x+1))

What is the first derivative of 4xln(2x+1) ?

The first derivative of 4xln(2x+1) is 4(ln(2x+1)+(2x)/(2x+1))

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derivative of

4 x ln (2 x + 1)

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

Solution steps

\frac{d}{d x} (4 x ln (2 x + 1))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \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)

= 4 (\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}

= 4 (1 \cdot ln (2 x + 1) + \frac{2}{2 x + 1} x)

Simplify

4 (1 \cdot ln (2 x + 1) + \frac{2}{2 x + 1} x) : 4 (ln (2 x + 1) + \frac{2 x}{2 x + 1})

= 4 (ln (2 x + 1) + \frac{2 x}{2 x + 1})

\frac{d}{d q} (2600 - 13 q)

cos (x) + 1

\frac{1}{( a - x )}

(4 - 3 x)^{10}

\frac{x ^{3} + 1}{x ^{3} + 8}

What is the derivative of 4xln(2x+1) ?
The derivative of 4xln(2x+1) is 4(ln(2x+1)+(2x)/(2x+1))
What is the first derivative of 4xln(2x+1) ?
The first derivative of 4xln(2x+1) is 4(ln(2x+1)+(2x)/(2x+1))