What is the derivative of 3/(log_{8(x)}) ?

The derivative of 3/(log_{8(x)}) is -1/(ln(2)xlog_{8)(x)^2}

What is the first derivative of 3/(log_{8(x)}) ?

The first derivative of 3/(log_{8(x)}) is -1/(ln(2)xlog_{8)(x)^2}

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\frac{d}{d x} (\frac{3}{lo g _{8} ( x )})

- \frac{1}{ln ( 2 ) x lo g _{8} ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3}{lo g _{8} ( x )})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{lo g _{8} ( x )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 3 \frac{d}{d x} (lo g_{8} (x)^{- 1})

Apply the chain rule:

- \frac{1}{( lo g _{8} ( x ) ) ^{2}} \frac{d}{d x} (lo g_{8} (x))

= - \frac{1}{( lo g _{8} ( x ) ) ^{2}} \frac{d}{d x} (lo g_{8} (x))

\frac{d}{d x} (lo g_{8} (x)) = \frac{1}{3 ln ( 2 ) x}

= 3 (- \frac{1}{( lo g _{8} ( x ) ) ^{2}} \cdot \frac{1}{3 ln ( 2 ) x})

Simplify

3 (- \frac{1}{lo g _{8} ( x ) ^{2}} \cdot \frac{1}{3 ln ( 2 ) x}) : - \frac{1}{ln ( 2 ) x lo g _{8} ( x ) ^{2}}

= - \frac{1}{ln ( 2 ) x lo g _{8} ( x ) ^{2}}

What is the derivative of 3/(log_{8(x)}) ?
The derivative of 3/(log_{8(x)}) is -1/(ln(2)xlog_{8)(x)^2}
What is the first derivative of 3/(log_{8(x)}) ?
The first derivative of 3/(log_{8(x)}) is -1/(ln(2)xlog_{8)(x)^2}