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Differentiation

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  1. 1.If y= ^-1((3 x-4 x)/(4 x+3 x))+2 ^-1(x1+√1-x^2), then (dy)/(dx) at x=√32 is equal to :
  2. 2.Let f(x)=x^3+x^2f^'(1)+2xf^''(2)+f^'''(3), x R.
  3. 3.y(x)=vmatrix x x x+ x+1 27 28 27 1 1 1 vmatrix,x Rd^2ydx^2+y
  4. 4.Let f:R R be a twice differentiable function such that ( x y)(f(2x+2y)-f(2x-2y))=( x y)(f(…
  5. 5.Let f:(0,) R be a function which is differentiable at all points of its domain and satisfi…
  6. 6.If _ey=3 ^-1x, then (1-x^2)y^''-xy^' at x=(1)/(2) is equal to
  7. 7.Let f(x)=ax^3+bx^2+cx+41 be such that f(1)=40,f^'(1)=2 and f^''(1)=4.
  8. 8.Suppose for a differentiable function h,h(0)=0,h(1)=1 and h^'(0)=h^'(1)=2.
  9. 9.f(x)= array|c|c| x^3 ((1)/(x)), & x 0 0 & ,x=0 array
  10. 10.If y( )=(2 + 2 )/( 3 +4 2 +5 +2), then at =( )/(2),y^''+y^'+y is equal to :
  11. 11.Let f(x)=x^5+2e^x/4 for all x R.
  12. 12.Let f:R-0 R be a function satisfying f((x)/(y))=(f(x))/(f(y)) for all x,y,f(y) 0.
  13. 13.Let g:R R be a non constant twice differentiable function such that g^'((1)/(2))=g^'((3)/(…
  14. 14.If f(x)=vmatrix 2 ^4x 2 ^4x 3+ ^22x 3+2 ^4x 2 ^4x ^22x 2 ^4x 3+2 ^4x ^22x vmatrix, then (1…
  15. 15.y= _e(1-x^21+x^2),-1<x<1x=(1)/(2)225(y^'-y^'')
  16. 16.Suppose f(x)=(2^x+2^-x) x ^-1(x^2-x+1)(7x^2+3x+1)^3.
  17. 17.For the differentiable function f:R-0 R, let 3f(x)+2f((1)/(x))=(1)/(x)-10, then |f(3)+f^'(…
  18. 18.Let f(x)= x+ x-√2 x- x,x [0, ]-( )/(4).
  19. 19.If 2 x^y+3 y^x=20, then [(d y)/(d x)] at (2,2) is equal to :
  20. 20.Let f:R R be a thrice differentiable odd function satisfying f^'(x) 0,f^''(x)=f(x),f(0)=0,…
  21. 21.Let f:R R be a thrice differentiable function such that f(0)=0,f(1)=1,f(2)=-1,f(3)=2 and f…
  22. 22.If y=(x+1)(x^2-x)xx+x+x+(1)/(15)(3 ^2x-5) ^3x, then 96y^'(( )/(6)) is equal to : Answer: 1…
  23. 23.Let f(x)=x^3+x^2f^'(1)+xf^''(2)+f^'''(3),x R.
  24. 24.Let f(x)= _k=1^10kx^k,x R.
  25. 25.If [f( x ) = x^n,] then the value of [f( 1 ) - f'( 1 ) 1! + f''( 1 ) 2! - f'''( 1 ) 3! + .…
  26. 26.If [x = e^y + e^y + e^y + ..... ] , x > 0, then [dy dx] is
  27. 27.Let y be an implicit function of x defined by [x^2x - 2x^x ,y - 1 = 0].
  28. 28.[d^2x dy^2] equals:
  29. 29.If g is the inverse of a function f and [f'( x ) = 1 1 + x^5,] then [g'( x )] is equal to:
  30. 30.If for [x ( 0,1 4 )], the derivatives of [ ^ - 1( 6x x 1 - 9x^3 )] is [ x .g( x )], then […
  31. 31.If y = [[ x + x^2 - 1 ]^15 + [ x - x^2 - 1 ]^15,] then (x2 - 1) [d^2y dx^2 + xdy dx] is eq…
  32. 32.If f(x) = sin-1 [( 2 3^x 1 + 9^x ),] then f'[( - 1 2 )] equals :
  33. 33.If x2 + y2 + sin y = 4, then the value of [d^2y dx^2] at the point (-2,0) is :
  34. 34.If [x = 2^ ec^ - 1 ] and [y = 2^sec^ - 1t ,,( | t | 1 ),] then [dy dx] is equal to :
  35. 35.Let f(x) = loge(sin x), (0 < x < [ ]) and g(x) = sin--1 (e--x ), (x [ ] 0).
  36. 36.Let f : R [ ] R be a function such that f(x) = x3 + x2f'(1) + xf''(2) + f'''(3), x [ ] R.
  37. 37.If xloge(logex) - x2 + y2 = 4(y > 0), then [dy dx] at x = e is equal to :
  38. 38.If ey + xy = e, the ordered pair [( dy dx,d^2y dx^2 )] at x = 0 is equal to :
  39. 39.For x > 1, if (2x)2y = 4e2x-2y, then (1 + loge 2x)2 [dy dx] is equal to :
  40. 40.If f(1) = 1, f'(1) = 3, then the derivative of f(f(f(x))) + (f(x))2 at x = 1 is :
  41. 41.If x = 3 tan t and y = 3 sec t, then the value of [d^2y dx^2] at t [ = 4,] is :
  42. 42.If y2 + loge (cos2x) = y, [x ( - 2, 2 )], then :
  43. 43.If [( a + 2 b x )( a - 2 b y ) = a^2 - b^2] where a > b > 0, then [dx dy,,at( 4, 4 )] is :
  44. 44.The derivative of [ ^ - 1( 1 + x^2 - 1 x )] with respect to [ ^ - 1( 2x 1 - x^2 1 - 2x^2 )…
  45. 45.Let y = y(x) be a function of x satisfying [y 1 - x^2 = k - x 1 - y^2 ] where k is a const…
  46. 46.If [y( ) = 2( + 1 + ^2 ) + 1 ^2 , ( 3 4, )] [dy d ,,at, = 5 6is] :
  47. 47.Let xk + yk = ak, (a, k > 0 ) and [dy dx + ( y x )^1 3 = 0], then k is:
  48. 48.Let f(x) = (sin(tan--1x) + sin(cot--1x))2 -- 1, |x| > 1.
  49. 49.Let f and g be differentiable functions on R such that fog is the identity function.
  50. 50.If [x = 2 - 2 ] and [y = 2 - 2 ], [ [ 0,2 ]], then [d^2y dx^2] at [ ] = [ ] is :