If f(x) = [(a+x) / (b+x)] to the power a+b+2x, find f'(x) at x=0.

Asked by pratikbharadia | 28th 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  | 28th Dec, 2009, 12:06: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.