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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{( ln ( z ) ) ^{5}}{z} d z

\int e^{- 12 x} d x

x \to 5 lim (\frac{7 x}{x - 5})

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

x + \frac{5}{x}

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