CBSE Class 12-science Answered
If f(x) = [(a+x) / (b+x)] to the power a+b+2x, find f'(x) at x=0.
Asked by pratikbharadia | 28 Dec, 2009, 11:57: AM
Expert Answer
Taking log on both sides,
log f(x) = (a+b+2x) log[(a+x)/(b+x)] = (a+b+2x) [log(a+x) - log (b+x)]
Differentiating both sides w r t x,
f'(x)/f(x) = (a+b)[log(a+x) - log (b+x)] + (a+b+2x)[1/(a+x) - 1/(b+x)]
f(0) = (a/b)a+b
f'(0) = (a/b)a+b [(a+b) log (a/b) + (a+b) (1/a - 1/b)]
= (a/b)a+b(a+b) [log (a/b) + (b-a)/ab]
Regards,
Team,
TopperLearning.
Answered by | 28 Dec, 2009, 12:06: PM
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