What is the derivative of 1/(log_{3)(1-2x)} ?

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

What is the first derivative of 1/(log_{3)(1-2x)} ?

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

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derivative of

\frac{1}{lo g _{3} ( 1 - 2 x )}

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

Solution steps

\frac{d}{d x} (\frac{1}{lo g _{3} ( 1 - 2 x )})

Apply exponent rule:

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

= \frac{d}{d x} (lo g_{3} (1 - 2 x)^{- 1})

Apply the chain rule:

- \frac{1}{( lo g _{3} ( 1 - 2 x ) ) ^{2}} \frac{d}{d x} (lo g_{3} (1 - 2 x))

= - \frac{1}{( lo g _{3} ( 1 - 2 x ) ) ^{2}} \frac{d}{d x} (lo g_{3} (1 - 2 x))

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

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

Simplify

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

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

\frac{d}{d t} (t^{2} + t^{3})

\frac{d}{d t} (3 t^{2} - 5 cos^{3} (t))

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

y = 1 - 2 x - x^{2}

\frac{x ^{3} + 8}{3}

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