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}} (- \frac{1}{5})

Simplify

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