What is the derivative of log_{8}(sqrt(x+9)) ?

The derivative of log_{8}(sqrt(x+9)) is 1/(6ln(2)(x+9))

What is the first derivative of log_{8}(sqrt(x+9)) ?

The first derivative of log_{8}(sqrt(x+9)) is 1/(6ln(2)(x+9))

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\frac{d}{d x} (lo g_{8} (x + 9))

\frac{1}{6 ln ( 2 ) ( x + 9 )}

Solution steps

\frac{d}{d x} (lo g_{8} (x + 9))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x + 9 )}{ln ( 8 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 8 )} \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}{ln ( 8 )} \cdot \frac{1}{x + 9} \cdot \frac{1}{2 x + 9}

Simplify

\frac{1}{ln ( 8 )} \cdot \frac{1}{x + 9} \cdot \frac{1}{2 x + 9} : \frac{1}{6 ln ( 2 ) ( x + 9 )}

= \frac{1}{6 ln ( 2 ) ( x + 9 )}

\int 13 sin^{2} (x co) s^{2} x d x

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\frac{d}{d x} \frac{1}{( ( \frac{b}{2} + x ) ^{2} + a ^{2} ) ^{\frac{3}{2}}}

\int e^{x} 45 + e^{x} d x

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What is the derivative of log_{8}(sqrt(x+9)) ?
The derivative of log_{8}(sqrt(x+9)) is 1/(6ln(2)(x+9))
What is the first derivative of log_{8}(sqrt(x+9)) ?
The first derivative of log_{8}(sqrt(x+9)) is 1/(6ln(2)(x+9))