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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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