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Find the derivatives w.r.t. x : log[e^...

Find the derivatives w.r.t. x :
`log[e^(x)((x-2)/(x+2))^((3)/(4))]`

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The correct Answer is:
`(x^(2)-1)/(x^(2)-4)`
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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Find the derivatives w.r.t. x : log[e^(x)((x-2)/(x+2))^((3)/(4))]

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  2. Find the derivatives w.r.t. x : (5x)/(root(3)(1-x^(2)))+sin^(2)(2x+3...

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  3. Find the derivatives w.r.t. x : sqrt(1+sin x)+sqrt((1-x^(2))/(1+x^(...

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  4. Find the derivatives w.r.t. x : (1)/(sqrt(x+a)-sqrt(x+b))+x^(2)sin(x...

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  5. Find the derivatives w.r.t. x : log sqrt((1+cos^(2)x)/(1-e^(2x)))

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  6. Find the derivatives w.r.t. x : tan^(-1)((sinx)/(1+cosx))

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  7. Find the derivatives w.r.t. x : log(x)sinx

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  8. Find the derivatives w.r.t. x : log(sinx)x

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  9. Find the derivatives w.r.t. x : log(x) tan x

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  10. Find the derivatives w.r.t. x : log(sin x)(sec x)+10^(x^(2))

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  11. Find the derivatives w.r.t. x : tan^(-1)((cosx)/(1+sinx))+sin(logx)

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  12. Find the derivatives w.r.t. x : (1+x)^(x)

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  13. Find the derivatives w.r.t. x : x^(sinx)

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  14. Find the derivatives w.r.t. x : x^(cos^(2)x)

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  15. Find the derivatives w.r.t. x : x^(y)=e^(x)

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  16. Find the derivatives w.r.t. x : (x^(x))^(x)

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  17. Find the derivatives w.r.t. x : (tan x)^(sin x) " when " x=(pi)/(4)

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  18. Find the derivatives w.r.t. x : x^(cos^(-1)x)

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  19. Find the derivatives w.r.t. x : x^(e^(x))

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  20. Find the derivatives w.r.t. x : (log x)^(cosx)

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