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  If     f(x)=[(c+x)/(d+x)]c+d+2x Show …

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If     f(x)=[(c+x)/(d+x)]c+d+2x

Show that f'(0)=[c+d]^c+d  [2 log c/d+(d^2-c^2)/cd]

please solve this problem

 

  • 1 answers

Soumya Ghoshal 6 years, 8 months ago

logf(x) =(c+d+2x)(log(c+x)-log(d+x))

or,f'(x)/f(x)=2(log(c+x)-log(d+x))+(c+d+2x)                       ((1/c+x)-(1/d+x))

f'(0)=f(0)*2(logc-logd)+(c+d)(1/c-1/d)

f'(0)=(c/d)^(c+d)[2{log(c/d)+(c+d)(d-                      c)/cd}]

f'(0)=(c/d)^(c+d)[2{log(c/d)+(d^2-c^2)/cd}]

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