What is the derivative of-2log_{6}(x) ?

The derivative of-2log_{6}(x) is -2/(ln(6)x)

What is the first derivative of-2log_{6}(x) ?

The first derivative of-2log_{6}(x) is -2/(ln(6)x)

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\frac{d}{d x} (- 2 lo g_{6} (x))

- \frac{2}{ln ( 6 ) x}

Solution steps

\frac{d}{d x} (- 2 lo g_{6} (x))

Take the constant out:

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

= - 2 \frac{d}{d x} (lo g_{6} (x))

Apply the derivative log rule:

\frac{d}{d x} (lo g_{a} (x)) = \frac{1}{x ln ( a )}

= - 2 \cdot \frac{1}{x ln ( 6 )}

Simplify

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

= - \frac{2}{ln ( 6 ) x}

e^{9 x}

\frac{d y}{d x}, x y = 9 + x^{2} y

\frac{d}{d x} (ln (\frac{x}{x + 2}))

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\frac{d}{d x} (sin (x) - e^{- x})

What is the derivative of-2log_{6}(x) ?
The derivative of-2log_{6}(x) is -2/(ln(6)x)
What is the first derivative of-2log_{6}(x) ?
The first derivative of-2log_{6}(x) is -2/(ln(6)x)