6.25. Find the derivative $y_{x}^{\prime}$ of the function $x(t)=\arcsin t$, $y=3^{\cos t}$.
Solution.

$$
y_{x}^{\prime}(x)=\frac{\left(3^{\cos t}\right)_{t}^{\prime}}{(\arcsin t)_{t}^{\prime}}=\frac{3^{\cos t} \cdot \ln 3 \cdot(-\sin t)}{\frac{1}{\sqrt{1-t^{2}}}}=-3^{\cos t} \cdot \ln 3 \cdot \sin t \cdot \sqrt{1-t^{2}}
$$

## DEFINITION OF TANGENT AND NORMAL TO THE GRAPH OF A FUNCTION