Eamcet - Maths - Differentiation

If √1-x2+√1-y2=a(x-y) then dy/dx=

A.  √(1+y2)/√(1+x2)

B.  √(1+x2)/√(1+y2)

C.  √(1-y2)/√(1+x2)

D.  √(1-y2)/√(1-x2)

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d/dx{Sin-12x/1+x2}=

A.  -1/2√(1-x2)

B.  1/1+x2

C.  2/1+x2

D.  2/√(1-x2)

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If y=√(cos x+y) then dy/dx=

A.  sin x/x-1

B.  sin y/1-x

C.  sin x/1-2y

D.   ny/2x-1

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The derivative of Sin-1 cos x w.r.to x is

A.  0

B.  1

C.  -1

D.  2

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If y= acos (log x)+b sin (log x) then x2y2+xy1+y=

A.  0

B.  1

C.  2

D.  none

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If f(x)=x2sin(1/x) for x≠0, f(0)=0 then

A.  f and f1are continuous at x=0

B.  f is derivative at x=0 and f1is not continuous at x=0

C.  f is derivable at x=0 and f1 is continuous at x=0

D.   noneof these

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The derivative of Sin-12x/1+x2 w.r.to Tan-12x/1-x2is

A.  0

B.  1

C.  -1

D.  2

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If y= x2+1/(x2+1/x2+....∞), then dy/dx=

A.  2xy2/y2+1

B.  2xy/y2+1

C.  2x/y2+1

D.  2/y2+1

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If x= et(cos t +sin t), y= et(cos t-sin t) then dy/dx=

A.  tan t

B.  –tan t

C.  tan (3t/2)

D.  –cot (3θ/2)

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If x-y=Sin-1 x-Sin-1 y then dy/dx=

A.  √y(4x√x-√y)/√x(2√y+√x)

B.  √y(1-2√xy-y)/√x(1+2√xy+x)

C.  2x+3/2y+5

D.  √1-y2-√(1-x2)(1-y2)/√(1-x2)-√(1-x2)(1-y2)

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If |x|

A.  1/(1+x)2

B.  2/(1+x)3

C.  -2/(1+x)3

D.  none

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d/dx{(√(a2+x2)+ √(a2-x2))/ (√(a2+x2)- √(a2-x2))}

A.  (2a2/x2){1+a2/√(a4-x4)}

B.  (2a2/x3){1+a2/√(a4-x4)}

C.  1+a2/√(a4-x4)

D.  1-a2/√(a4+x4)

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d/dx{Tan-1√(1-x/1+x)}=

A.  1/2(1+x2)

B.  -1/2√1-x2

C.  3/1+x2

D.  1/2√1-x2

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If x2-xy+y2=1 and y’’(1)=

A.   -6

B.  2/3

C.  3/2

D.  -2/3

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d/dx{Tan-1(x-√x/1+x3/2}=

A.  (1/1+x2)-(1/2(1+x)√x)

B.  1/2√(1+x2)

C.  1/√1+x2

D.  1/2√1-x2

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If 3x2+4xy+2y2+x-8=0 and dy/dx at (1,1),(1,2),(2,-1),(-1,3) are respectively A,B,C,D then the descending order of A,B,C,D is

A.  A,B,C,D

B.  B,C,A,D

C.  C,A,B,D

D.  B,A,C,D

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d/dx { log√(cosec x+1)-√(cosec x-1)}=

A.  cosec x

B.  2 cosec x

C.  1/2 cosec x

D.  cot x

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The derivative of (sin x)x w.r.to x is

A.  (sin x)x[x cot x+ log sin x]

B.  (sin x)x[x cot x-log sin x]

C.  -(sin x)x[x cot x+ log sin x]

D.  -(sin x)x[x cot x-log sin x]

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If |x|

A.  p/q.1/(1-x)p/q+1

B.  (p/q)1/(1-x)p/q

C.  (1-x)-p/q-1

D.  none

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Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then

A.  a=-1/2,b=3/2

B.  a=-1/2,b=1/2

C.  a=1,b=-1

D.  a=1/2,b=1/2

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The derivative of Tan-1√(1+x2)-1/x w.r.to Tan-12x√(1-x2)/(1-2x2) at x=0 is

A.  1

B.  1/2

C.  1/4

D.  1/8

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If cos x/2 . cos x/22. Cos x/23.... cos x/2n= sin x/2nsin (x/2n) then (1/22)sec2x/2+(1/24) sec2x/22...(1/22n)sec2x/2n=

A.  (1/22n)cosec2x/2n+cosec2x

B.  –(1/22n)cosec2x/2n+cosec2x

C.  cosec2x/2n+cosec2 x

D.  none

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If ax2+2hxy+by2=1 then (hx+by)3y2=

A.  0

B.  1

C.  k2-ab

D.  ab-h2

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d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=

A.  1

B.  -1

C.  1/2

D.  -1/2

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If sin2 mx+cos2 ny=a2 then dy/dx=

A.  m sin (2mx)/nsin(2ny)

B.  m cos(2mx)/nsin(2ny)

C.  mcos(2mx)/n cos(2ny)

D.  m sin(2mx)/n cos (2ny)

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If x=sin-1t, y= √(1-t2) then d2y/dx2=

A.  -√(1-t2)

B.  -1

C.  t2

D.  none

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The derivative of cos hx/2w.r.to x is

A.  2 sech2 2x

B.  3 cosh 3x

C.  1/2 sin hx/2

D.  -5 cosech25x

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If P(x)is a polynomial of 3rd degree and P’’(1)=0, P’’’(1)=6 then P’’(0)=

A.  0

B.  6

C.  -6

D.  none

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Let f(x+y)= f(x)f(y) for all x,y ε R. If f is differentiable at x=0, then

A.  f is differentiable everywhere

B.  f is not differentiable everywhere

C.  f is not differentiable at x=1

D.  f is not differentiable everywhere

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The derivative of (log x)xw.r.to x is

A.  (log x)x-1[1+log x log (log x)]

B.  (log x)x-1[1-log x log(log x)]

C.  –(log x)x-1[1+log x log (log x)]

D.  –(log x)x-1[1-log x log(log x)]

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