What is the derivative of ln(sqrt(x+9)) ?

The derivative of ln(sqrt(x+9)) is 1/(2(x+9))

What is the first derivative of ln(sqrt(x+9)) ?

The first derivative of ln(sqrt(x+9)) is 1/(2(x+9))

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derivative of

ln (x + 9)

\frac{1}{2 ( x + 9 )}

Solution steps

\frac{d}{d x} (ln (x + 9))

Apply the chain rule:

\frac{1}{x + 9} \frac{d}{d x} (x + 9)

= \frac{1}{x + 9} \frac{d}{d x} (x + 9)

\frac{d}{d x} (x + 9) = \frac{1}{2 x + 9}

= \frac{1}{x + 9} \cdot \frac{1}{2 x + 9}

Simplify

\frac{1}{x + 9} \cdot \frac{1}{2 x + 9} : \frac{1}{2 ( x + 9 )}

= \frac{1}{2 ( x + 9 )}

\frac{d}{d x} (\frac{x ^{9}}{9} - \frac{x ^{7}}{7})

x \to 1 lim (\frac{e ^{x^{2} - 1}}{x ^{2} - 3 x + 2})

\frac{d y}{d x} = \frac{( y - 1 )}{x ^{2}}

d er i v a t i v e 6 cos (2 x)

\int \frac{100}{36 + 25 x ^{2}} d x

What is the derivative of ln(sqrt(x+9)) ?
The derivative of ln(sqrt(x+9)) is 1/(2(x+9))
What is the first derivative of ln(sqrt(x+9)) ?
The first derivative of ln(sqrt(x+9)) is 1/(2(x+9))