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

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

A

`(logx)^x[1/(logx)+log(logx)]+(cosx)^(logx)[1/xlog(cosx)-logx.tanx]`

B

`(cosx)^(logx)[log(cosx)-cotx.logx]+(logx)^(logx)[1+log(logx)]`

C

`((cos x)^("log" x) + ("log x")^(x))["log" x."cos " x + x " log" x]`

D

`(logx)^(x)[logx+log(logx)](cosx)^(logx)`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan...

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

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

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

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

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

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

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

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

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

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

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

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  14. x = cos^(-1)((1)/(sqrt(1+t^(2)))),y = sin^(-1)((t)/(sqrt(1+t^(2))))rAr...

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  15. x ^(2) + y^(2) = t + 1/t, x ^(4) + y^(4) = t ^(2) + (1)/( t ^(2)) impl...

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  16. A function is represented parametrically by the equations x=(1+t)/(t^3...

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  17. If x+ y = sin(x+y) then (dy)/(dx) =

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  18. If cos y =x cos (a + y) then (dy)/(dx)=

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  19. If xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

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  20. If sin (x+y) = log (x + y), then dy //dx =

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