What is the derivative of arccos(x/5) ?

The derivative of arccos(x/5) is -1/(sqrt(25-x^2))

What is the first derivative of arccos(x/5) ?

The first derivative of arccos(x/5) is -1/(sqrt(25-x^2))

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\frac{d}{d x} (arccos (\frac{x}{5}))

- \frac{1}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (arccos (\frac{x}{5}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \frac{d}{d x} (\frac{x}{5})

= - \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= - \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \cdot \frac{1}{5}

Simplify

- \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \cdot \frac{1}{5} : - \frac{1}{25 - x ^{2}}

= - \frac{1}{25 - x ^{2}}

What is the derivative of arccos(x/5) ?
The derivative of arccos(x/5) is -1/(sqrt(25-x^2))
What is the first derivative of arccos(x/5) ?
The first derivative of arccos(x/5) is -1/(sqrt(25-x^2))