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If y =cot^(-1) (1-x+x^2) , then (dy)/(dx...

If `y =cot^(-1) (1-x+x^2)` , then `(dy)/(dx)` =

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
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  3. If y =cot^(-1) (1-x+x^2) , then (dy)/(dx) =

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  4. f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

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  5. f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

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  6. If y =(logx)^(x) then (dy)/(dx) =

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  7. If x^(m) y^(n)=(x+y)^(m+n) , then dy/dx is equal to

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  8. If y = 2^(2 ^(x)), then (dy)/(dx) =

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  9. If y = (sinx)^(x) then (dy)/(dx) =

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  10. If y=x^(cosx) then (dy)/(dx)=

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  11. d/(dx){x^(tanx)} =

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  12. If y = (ax+b)^(cx+d) then (dy)/(dx) =

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  13. The derivative of y = (1-x) (2-x) (3-x) ....(n-x) at x = 1 is

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  14. If y = log {((1 +x)/(1-x )) ^(1//4) } -1/2 Tan ^(-1) (x ), then (dy)/(...

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  17. d/(dx)[(cosx)^(logx)+(logx)^(x)] =

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  18. If f(x) = cos x cos 2x cos 2^2 x cos^(2^3) x .....cos 2^(n-1) x and n ...

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  19. d/(dx)(log(e^x((x-2)/(x+2))^(3//4))) equal to

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  20. y = log^(n)x x where log^(n) means log.log.log ....(repeated n times) ...

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