What is the derivative of 1/(arccos(3x)) ?

The derivative of 1/(arccos(3x)) is 3/(arccos^2(3x)sqrt(1-9x^2))

What is the first derivative of 1/(arccos(3x)) ?

The first derivative of 1/(arccos(3x)) is 3/(arccos^2(3x)sqrt(1-9x^2))

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\frac{d}{d x} (\frac{1}{arccos ( 3 x )})

\frac{3}{arccos ^{2} ( 3 x ) 1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{arccos ( 3 x )})

Apply exponent rule:

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

= \frac{d}{d x} (arccos^{- 1} (3 x))

Apply the chain rule:

- \frac{1}{( arccos ( 3 x ) ) ^{2}} \frac{d}{d x} (arccos (3 x))

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

\frac{d}{d x} (arccos (3 x)) = - \frac{3}{1 - 9 x ^{2}}

= - \frac{1}{( arccos ( 3 x ) ) ^{2}} (- \frac{3}{1 - 9 x ^{2}})

Simplify

- \frac{1}{arccos ^{2} ( 3 x )} (- \frac{3}{1 - 9 x ^{2}}) : \frac{3}{arccos ^{2} ( 3 x ) 1 - 9 x ^{2}}

= \frac{3}{arccos ^{2} ( 3 x ) 1 - 9 x ^{2}}

What is the derivative of 1/(arccos(3x)) ?
The derivative of 1/(arccos(3x)) is 3/(arccos^2(3x)sqrt(1-9x^2))
What is the first derivative of 1/(arccos(3x)) ?
The first derivative of 1/(arccos(3x)) is 3/(arccos^2(3x)sqrt(1-9x^2))