Example 2. Find the derivative of the function $y=a^{x^{2}}$.
Solution. By formula ( $2.12^{\prime}$ ) we get

$$
\left(a^{x^{2}}\right)^{\prime}=a^{x^{2}} \cdot \ln a \cdot\left(x^{2}\right)^{\prime}=a^{x^{2}} \cdot \ln a \cdot 2 x=2 \ln a \cdot x \cdot a^{x^{2}}
$$