What is the derivative of y=ln(sqrt(x+6)) ?

The derivative of y=ln(sqrt(x+6)) is 1/(2(x+6))

What is the first derivative of y=ln(sqrt(x+6)) ?

The first derivative of y=ln(sqrt(x+6)) is 1/(2(x+6))

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derivative of

y = ln (x + 6)

\frac{1}{2 ( x + 6 )}

Solution steps

\frac{d}{d x} (ln (x + 6))

Apply the chain rule:

\frac{1}{x + 6} \frac{d}{d x} (x + 6)

= \frac{1}{x + 6} \frac{d}{d x} (x + 6)

\frac{d}{d x} (x + 6) = \frac{1}{2 x + 6}

= \frac{1}{x + 6} \cdot \frac{1}{2 x + 6}

Simplify

\frac{1}{x + 6} \cdot \frac{1}{2 x + 6} : \frac{1}{2 ( x + 6 )}

= \frac{1}{2 ( x + 6 )}

What is the derivative of y=ln(sqrt(x+6)) ?
The derivative of y=ln(sqrt(x+6)) is 1/(2(x+6))
What is the first derivative of y=ln(sqrt(x+6)) ?
The first derivative of y=ln(sqrt(x+6)) is 1/(2(x+6))