Answer
$$\frac{e}{2}.$$
Work Step by Step
By differentiation, we have
$$f'(g(x))g'(x)=2xe^{x^2}$$
hence we have
$$f'(g(1))g'(1)=f'(2) 4=2e \Longrightarrow f'(2)=\frac{e}{2}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 11
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