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

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

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

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

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derivative of

ln (x + 1)

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x + 1} \cdot \frac{1}{2 x + 1}

Simplify

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

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

\frac{d y}{d t} = 0.3 y + 26 e^{0.3 t}

\frac{8 x ^{2} + 4 x + 8}{x}

\frac{\partial}{\partial x} (x^{2})

f (x) = 6 ln (sec (x) + tan (x))

\int p (p + 5)^{7} d p

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