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(d)/(dx) [ log{e^(x) ((x-2)/(x +2))^(3//...

`(d)/(dx) [ log{e^(x) ((x-2)/(x +2))^(3//4)}]` is equal to

A

1

B

`(x^(2) +1)/(x^(2) -4)`

C

`(x^(2) -1)/(x^(2) -4)`

D

`e^(x) (x^(2) -1)/(x^(2) -4)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` y = log{e^(x)((x-2)/(x +2))^(3//4)}= loge^(4) + log((x-2)/(x+2))^(3//4)`
` rArr y =x + (3)/(4) [log(x-2) - log(x + 2)]`
On differentiating both sides w.r.t.x., we get
`(dy)/(dx) = 1 + (3)/(4) [(1)/(x-2) -(1)/(x+2)]=1+(3)/((x^(2) -4)) rArr (dy)/(dx) = (x^(2) -1)/(x^(2) -4)`
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  • d/dx[log{e^x((x-2)/(x+2))^(8//4)}] is equal to

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