d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=
1
-1
1/2
-1/2
If xy(x+y)=2 then dy/dx=
(y/x)1/3
- (y/x)1/3
x2-ay/ax-y2
–y(2x+y)/x(x+2y)
If y= a cos mx+b sin m=mx, then d2y/dx2=
–m2y
m2y
my2
my
If f(x)= x(√x-√(x+1)) then
f(x) is continuous but not differentiable at x=0
f(x) is differentiable at x=0
f(x) is not differentiable
none
If y= xsin x+(sin x)x then dy/dx=
e2
0
3/2
d/dx{sin2((1-x2)/(1+x2))}
4x/(1+x2)2sin 2 (1-x2/1+x2)
4x/(1-x2)2sin (1-x2/1+x2)
- 4x/(1+x2)2sin 2 (1-x2/1+x2)
4x/(1-x2)2sin 2 (1-x2/1+x2)
If y= x2+1/(x2+1/x2+....∞), then dy/dx=
2xy2/y2+1
2xy/y2+1
2x/y2+1
2/y2+1
d/dx{Tan-1 1/√x2-1}=
-1/x√(x2-1)
1/x√(x2-1)
2/(x√x2+1)
-2/x√(x2+1)
If y= x log|x+√(1+x2)|-√(1+x2) then dy/dx=
log(x-√(1-x2)
1/2 log(x+√(1+x2)
sinh-1 x
If x= 2/t2, y=t3-1, then d2y/dx2=
15t2
15/16t2
15t2/16
16t2
The derivative of Sin-12x/1+x2 w.r.to Tan-12x/1-x2is
2
If x=e2tcos 3t, then d2x/dt2 at t=π/2 is
12eπ
-12e-π
6eπ
-6eπ
d/dx{Tan-13x-x3/1-3x2}=
1/2(1+x2)
-1/2√1-x2
3/1+x2
1/2√1-x2
d/dx{cos[2 sin-1(cos x)]}=
2 sin 2 x
3 cos 2 x
If f(x)=x2sin(1/x) for x≠0, f(0)=0 then
f and f1are continuous at x=0
f is derivative at x=0 and f1is not continuous at x=0
f is derivable at x=0 and f1 is continuous at x=0
noneof these
The derivative of (log x)xw.r.to x is
(log x)x-1[1+log x log (log x)]
(log x)x-1[1-log x log(log x)]
–(log x)x-1[1+log x log (log x)]
–(log x)x-1[1-log x log(log x)]
The derivative of Tan-1√(1+x2)-1/x w.r.to Tan-12x√(1-x2)/(1-2x2) at x=0 is
1/4
1/8
If f(x)=x2+x2/(1+x2)+x2/(1+x2)2+...+x2/(1+x2)n+... then x=0
f(x) has no limit
f(x) is dis continuous
f(x) is continuous but not differentiable
f(x) is differentiable
The derivative of √(tan x+√tan x) w.r.t x is
sec2x[1+2√tan x]/(4√tan2 x+ tan x √tan x)
sec2 x[1-2√tan x]/ (4√tan2 x+ tan x √tan x)
sec x[1+2√tan x]/ (4√tan2x+tan x √tan x)
sec x[1-2√tan x]/ (4√tan2x+tan x √tan x)
If x2-xy+y2=1 and y’’(1)=
-6
2/3
-2/3
The derivative of √(Tan-1 x) w.r.to x is
1/2(1+x2)√Tan-1 x
1/2(1-x2)√Tan-1 x
1/2(1+x2) Tan-1 x
1/2(1-x2) Tan-1 x
d/dx{Tan-1√(1-cos x)/(1+cos x)}=
If x2+y2=a2 then (1+y12)3/2/|y2|=
a2
a
1/a
d/dx{Tan-1(x/1-√1-x2)}=
Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then
a=-1/2,b=3/2
a=-1/2,b=1/2
a=1,b=-1
a=1/2,b=1/2
The derivative of Sin-1(3x-4x3) w.r.to Tan-1x/√ (1-x2) is
3
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,B,C,D
B,C,A,D
C,A,B,D
B,A,C,D
If y=2 Tan-1(x√2/1-x2)+log(1+x√2+x2/1-x√2+x2), then dy/dx=
1/1+x4
2/1+x4
2√2/1+x4
4√2/1+x4
d/dx{log(x2/ex)}=
2/x+1
2/x-1
-2/x+1
If xy=c2 then dy/dx=
x/y
–y/x
–x/y
y/x