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Let f(x)=(x-a)(x-b)(x-c) then prove that f`(x)/f(x)=1/(x-a)+1/(x-b)+1/(x-c)

Let f(x)=(x-a)(x-b)(x-c) then prove that f`(x)/f(x)=1/(x-a)+1/(x-b)+1/(x-c)

Grade:11

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
f(x) = (x-a)(x-b)(x-c)
f'(x) = (x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a)
f'(x)/f(x) = [(x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a)]/(x-a)(x-b)(x-c) = 1/(x-a) + 1/(x-b) + 1/(x-c).
 
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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