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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = ln (2 x + 1)

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int x^{13} e^{x^{14}} d x

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

x \to - 8 lim (2)

\frac{d}{d x} (5 x - 9 x^{2})

\frac{d}{d x} (\frac{x + 4}{x ^{2} + 4})

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