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

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

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

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

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derivative of

y = 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}{d x} (2 e^{- 2 x})

\frac{d}{d x} (cos^{- 2} (x))

\frac{d}{d x} ((3 x^{2} + 7 x)^{4})

f (x) = x^{3} - 9 x, at x = 3

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

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