use logarithmic differentiation to find dy/dx?

Question

y= ((x+2)sqrt(1-x^2))/4x^3

Answer 1

y= ((x+2)sqrt(1-x^2))/4x^3

taking log to the base e

ln(y) = ln(x+2) + (1/2) ln(1-x^2) - ln(4) - 3 ln(x)

diff w.r.t.x

(1/y)(dy/dx)={1/(x+2)} +(1/2) {1/ (1-x^2) }*{-2*x} - 0 -(3/x)

(dy/dx) = y[{ 1/(x+2) } - {x / (1-x^2) } - (3/x) ]


substitute for y and simplify if necessary

Answer 2

I did this once but my head hurt for a week. If no one else reply's I'll do it ............."sigh" :-)

Damn! I hate people who can do these like ducks do water LOL

Answer 3

if y=p/q
then y'=(p'q-q'p)/q^2

if f=u.v
then f'=u'.v+v'.u

p'=1.sqrt(1-x^2)+(-2x)/[2sqrt(1-x^2)](x+2)
q'=12x^2
Replace these values in y'

Answer 4

Come on friend you can do it!