What is the derivative of ln(sqrt(x+5)) ?

The derivative of ln(sqrt(x+5)) is 1/(2(x+5))

What is the first derivative of ln(sqrt(x+5)) ?

The first derivative of ln(sqrt(x+5)) is 1/(2(x+5))

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derivative of

ln (x + 5)

\frac{1}{2 ( x + 5 )}

Solution steps

\frac{d}{d x} (ln (x + 5))

Apply the chain rule:

\frac{1}{x + 5} \frac{d}{d x} (x + 5)

= \frac{1}{x + 5} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = \frac{1}{2 x + 5}

= \frac{1}{x + 5} \cdot \frac{1}{2 x + 5}

Simplify

\frac{1}{x + 5} \cdot \frac{1}{2 x + 5} : \frac{1}{2 ( x + 5 )}

= \frac{1}{2 ( x + 5 )}

What is the derivative of ln(sqrt(x+5)) ?
The derivative of ln(sqrt(x+5)) is 1/(2(x+5))
What is the first derivative of ln(sqrt(x+5)) ?
The first derivative of ln(sqrt(x+5)) is 1/(2(x+5))