What is the derivative of ln(sqrt(x+7)) ?

The derivative of ln(sqrt(x+7)) is 1/(2(x+7))

What is the first derivative of ln(sqrt(x+7)) ?

The first derivative of ln(sqrt(x+7)) is 1/(2(x+7))

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derivative of

ln (x + 7)

\frac{1}{2 ( x + 7 )}

Solution steps

\frac{d}{d x} (ln (x + 7))

Apply the chain rule:

\frac{1}{x + 7} \frac{d}{d x} (x + 7)

= \frac{1}{x + 7} \frac{d}{d x} (x + 7)

\frac{d}{d x} (x + 7) = \frac{1}{2 x + 7}

= \frac{1}{x + 7} \cdot \frac{1}{2 x + 7}

Simplify

\frac{1}{x + 7} \cdot \frac{1}{2 x + 7} : \frac{1}{2 ( x + 7 )}

= \frac{1}{2 ( x + 7 )}

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What is the derivative of ln(sqrt(x+7)) ?
The derivative of ln(sqrt(x+7)) is 1/(2(x+7))
What is the first derivative of ln(sqrt(x+7)) ?
The first derivative of ln(sqrt(x+7)) is 1/(2(x+7))