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

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

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

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

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derivative of

(2 x + 1) ln (x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

2 y d x + e^{- 3 x} d y = 0

\int \frac{x ^{2} + x - 5}{x ^{2} - 1} d x

\int \frac{5}{8 x ( x + 1 ) ^{2}} d x

\int - e^{- 2 y} + 1 d y

y = \frac{x}{x - 5}, (- 1, a)

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