## Problem Statement

Find the derivative $y_{x}^{\prime}$.

$$
\left\{\begin{array}{l}
x=\arcsin (\sin t) \\
y=\arccos (\cos t)
\end{array}\right.
$$
## Solution

$x_{t}^{\prime}=(\arcsin (\sin t))^{\prime}=t^{\prime}=1$

$y_{t}^{\prime}=(\arccos (\cos t))^{\prime}=t^{\prime}=1$

We obtain:

$y_{x}^{\prime}=\frac{y_{t}^{\prime}}{x_{t}^{\prime}}=\frac{1}{1}=1$

## Kuznetsov Differentiation 16-4