= Solution
The <multivariable chain rule> follows the change of both coordinates along the <parametric curve>:
$$
\frac{df}{ds}=f_x\frac{dx}{ds}+f_y\frac{dy}{ds},\qquad\frac{dx}{ds}=2s,\quad\frac{dy}{ds}=e^s.
$$
Substituting the <partial derivatives> from part (a), with $x=1+s^2$ and $y=e^s$, yields
$$
\boxed{\frac{df}{ds}=4s(1+s^2)(e^{4s}+e^{2s}+1)+4(1+s^2)^2e^{4s}+3e^{3s}+2(1+s^2)^2e^{2s}-3e^s.}
$$
The first term comes from changing $x$, and the remaining terms from changing $y$.
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