What is the derivative of arccos(3x) ?

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

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

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

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

- \frac{3}{1 - 9 x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x) = 3

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

Simplify

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

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

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