Let f and g be differentiable functions satisfying g ' (a) =2 , g(a) =b and fog=I (identity function) .Then f ' (b) is equal to _______ .
1/2
2
2/3
None of these
If f(x) = √1-x2 ,xε(0,1),then f '(x) is equal to _________ .
1/√1-x2
-x/√1-x2
√1-x2
√x2-1
The derivative of an even function is always ________ .
An odd function
An even function
Does not exist
If f(x)=x if x is rational = 1-x if x is irrational ,then
f is only right continuous at x=1/2
f is only left continuous at x=1/2
f is continuous at x=1/2
f is discontinuous at all points
If x=at2 , y=2at,then dy/dx is equal to ________ .
2at
2a
t
1/t
If y=t2 + t -1 , then dy/dx is equal to _______ .
2t+1
t2+t-1
0
not defined
The differential coefficient of log tan x is ________
2sec 2x
2 cosec 2 x
2 sec3x
2 cosec3x
If f(0) =0=g(0) and f ' (0)=6=g ' (0),then is given by ________ ?
1
12
-1
If f(x) = x tan-1 x , then f'(1) equals ________ .
1/2 + π/4
-1/2 + π/4
-1/2 -π/4
1/2 - π/4
The derivative of an odd function is always __________ .
