6.36. Find $y^{\prime \prime}(x)=f\left(e^{2 x}\right)$.

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6.36. Find $y^{\prime \prime}(x)=f\left(e^{2 x}\right)$.
Solution.

$$
\begin{aligned}
y^{\prime}(x) & =f^{\prime}\left(e^{2 x}\right) \cdot\left(e^{2 x}\right)^{\prime}=f^{\prime}\left(e^{2 x}\right) \cdot e^{2 x} \cdot 2 \\
y^{\prime \prime}(x) & =f^{\prime \prime}\left(e^{2 x}\right) \cdot e^{4 x} \cdot 4+f^{\prime}\left(e^{2 x}\right) \cdot e^{2 x} \cdot 4
\end{aligned}
$$