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

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

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

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

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derivative of

ln (x + 2)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int y^{2} e^{y^{3}} d y

\int x e^{\frac{x}{10}} d x

y = x^{18}

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

y = \frac{5}{x - 2}, (3, 5)

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