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Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))...

Find `(dy)/(dx)` if `y=log{e^x((x-2)/(x+2))^(3/4)}`

Text Solution

Verified by Experts

The correct Answer is:
`(x^(2)-1)/(x^(2)-4)`
`"Let "y=[log{e^(x)((x-2)/(x+2))^(3//4)}]=log e^(x)+log ((x-2)/(x+2))^(3//4)`
`=x+(3)/(4)[log (x-2)-log(x+2)]`
`therefore" "(dy)/(dx)=1+(3)/(4)[(1)/(x-2)-(1)/(x+2)]=1+(3)/((x^(2)-4))=(x^(2)-1)/(x^(2)-4)`
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