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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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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
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  4. If y = sqrt(sin + y ) "then" (dy)/(dx) is equal to

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  5. The differential coefficient of sin (cos (x^(2))) with respect to s i...

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  8. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

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  9. Derivative of log[log(log x^(5))] with respect to x is

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  11. If y = log(2) log(2) (x) , " then " (dy)/(dx) is equal to

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  12. If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

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  13. If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at ...

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  14. (d)/(dx)[log(e)e^(sin(x^(2)))] is equal to

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  15. If y=sqrt((1-x)/(1+x)), then (1-x^(2))(dy)/(dx)+y is equal to

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  16. Differential coefficient of sqrt(secsqrt (x)) is

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

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  18. Derivative of sqrte^(sqrt(x)) with respect to x is

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