6.23. Find the derivative $y_{x}^{\prime}(x)$ of the functions $x(t)=t^{2}$, $y(t)=\sin t^{3}$.
Solution.

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