Answer
$f'(x)=c_1+2c_2x+3c_3x^2+.....=\sum_{k=1}^{\infty} kc_kx^{k-1}$
Work Step by Step
Given $f(x)=\sum_{k=0}^{\infty} c_kx^k$ convergent for $|x|$
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 9 - Power Series - 9.4 Working with Taylor Series - 9.4 Exercises - Page 702: 5
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