# derivative of cos inverse

#### Understand the Problem

The question is asking for the derivative of the inverse cosine function, which involves calculus knowledge about derivatives and inverse trigonometric functions.

$-\frac{1}{\sqrt{1 - x^2}}$

The derivative of $\arccos(x)$ is $-\frac{1}{\sqrt{1 - x^2}}$

#### Steps to Solve

1. Identify the formula for the derivative of the inverse cosine function

The derivative of the inverse cosine function (also known as $\arccos(x)$) can be found using a known formula: $$\frac{d}{dx} \arccos(x) = -\frac{1}{\sqrt{1 - x^2}}$$

1. Understand the domain of the function

The function $\arccos(x)$ is defined for $-1 \leq x \leq 1$. This is important because the derivative also only applies within this domain.

The derivative of $\arccos(x)$ is $-\frac{1}{\sqrt{1 - x^2}}$

The inverse cosine function, $\arccos(x)$, is the angle whose cosine is $x$. The derivative of the inverse cosine shows how sensitive this angle is to changes in $x$ and is applicable within the domain $-1 \leq x \leq 1$.