vikas askiitian expert
Last Activity: 14 Years ago
y = 1 + a/(x-a) +bx/(x-a)(x-b) + cx2/(x-a)(x-b)(x-c)
breaking into different functions
y = 1 + f(x)1 + f(x)2 + f(x)3
f(x)1=a/(x-a) , f(x)2 =bx/(x-a)(x-b) & f(x)3 =cx2 /(x-a)(x-b)(x-c)
now
dy/dx= d/dx(1) + d/dx(f(x)1) +d/dx(f(x)2) +d/dx(f(x)3) ....................................1
now separatly differentiatiating f(x)1 , f(x)2 , f(x)3 by taking log
(taking log in both sides)
d/dx[log(f(x)1)] = d/dx(loga/x-a)
d/dx(f(x)1/f(x)1 = d/dx(loga - log(x-a) )
d/dx(f(x)1)=(-1/x-a)(f(x)1
d/dx(f(x)1) = -a/(x-a)2
now separatly differentiate each of these and put in eq 1 ,u will get the required result