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

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

A

`x^(cosx)((cosx)/(x)+sinx.logx)`

B

`x^(cosx)((cosx)/(x)-sinx.logx)`

C

`-x^(cosx)((cosx)/(x)-sinx.logx)`

D

`-x^(cosx)((cosx)/(x)+sinx.logx)`

Text Solution

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

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

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

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

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

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

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

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  8. f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan...

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  9. f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan...

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

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

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

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  14. If x = a cos^(4)t , y = b sin^(4)t then (dy)/(dx) at t = (3pi)/4 is

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  15. If x =cos^3 theta, y = sin^3 theta then sqrt(1+((dy)/(dx))^2)=

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  16. If x = a (t + sin t), y = a (1- cost) and (dx)/(dy) =cot p then p =

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  17. If x = "cosec" theta - sintheta, y = "cosec"^(n)theta - sin^(n) theta ...

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  18. If x = a (1-cos theta) , y = a ( theta + sin theta) then (dy)/(dx) a...

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  19. If x = a Sin 2 theta (1+Cos2 theta) , y = b Cos2 theta (1-Cos2 theta) ...

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  20. If x=(3at)/(1+t^2),y=(3at^2)/(1+t^2) then (dy)/(dx)=

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