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If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) the...

If `f(x)=cot^(-1)((x^(x)-x^(-x))/(2))` then f'(1) equals

A

`-1`

B

1

C

log 2

D

`-log 2`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x) = cot ^(-1) ((x^(x) - x^(-x))/(2)) = cot ^(-1) (((x)^(2x)-1)/(2x^(x)))`
` tan^(-1) ((2x^(x))/(-1 + (x^(x))^(2))) = 0 2 tan^(-1) x^(x)`
`rArr f'(x) = - (2)/(1 + (x^(x))^(2))xx x^(x) (1 + log_(e) x)`
`rArr f'(1) = - (2)/(1 +1)xx 1 (1 + log e ) = (-2)/(2) xx 1 = - 1`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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  2. If x=sectheta-costheta,y=sec^(10)theta-cos^(10)theta and (x^(2)+4)((dy...

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  3. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

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  4. If x^(y) = e^(2(x-y)), " then" f'(x) is equal to

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  5. If sqrt(1-x^(2n))+sqrt(1-y^(2n))=a^n(x^n-y^n), prove that y^(n-1)*sqr...

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  6. If f(x)=sin^(-1)(sinx)+cos^(-1)(sinx) and phi(x)=f(f(f(x))), then phi'...

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  7. Let x^cosy + y^cosx = 5, then

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  8. If y = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to

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  9. If y=tan^(-1)1/(1+x+x^2)+tan^(-1)1/(x^2+3x+3)+tan^(-1)1/(x^2+5x+7)++ u...

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  10. If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) , then (dy)/(dx) is equal to

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  11. If y = cos^(-1) ((2cos x - 3 sin x)/(sqrt(13))), " then" (dy)/(dx) i...

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  12. Let y=(x^(8)+x^(4)+1)/(x^(4)+x^(2)+1)."If"(dy)/(dx)=ax^(3)+bx. Then,

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  13. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

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  14. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))), then (dy)/(dx) is equal to

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  15. if y=sin^-1[sqrt(x-ax)-sqrt(a-ax)] then prove that 1/(2sqrtx sqrt(1-x)...

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  16. If y=log(x^(2)+4)(7x^(2)-5x+1), then (dy)/(dx) is equal to

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  17. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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  18. If x^(2) + y^(2) = a^(2) , then a is equal to

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  19. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) i...

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  20. If y = sin^(n) x cos nx, " then" (dy)/(dx) is

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