If for a continuous function `f,f(0)=f(1)=0,f^(prime)(1)=2` and `y(x)=f(e^x)e^(f(x))` , then `y^(prime)(0)` is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If f(x)={xsin(1/x) ,\ x!=0, then (lim)_(x->0)f(x) equals a. 1 b . 0 c. -1 d. none of these

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , write the value of (dy)/(dx) at x=0 .

If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to (a) 0 (b) 1/e (c) e (d) none of these

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

Let f(x)={(sinx^2)/x x!=0 0x=0, then f^(prime)(0^+)+f^(prime)(0^-) has the value equal to (a) 0 (b) 1 (c) 2 (d) None of these

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (a) f^(prime)(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f^(prime)(a^-) (d) none of these

If f(x)=(log)_(x^2)(logx), then f^(prime)(x) at x=e is 0 (b) 1 (c) 1/e (d) 1/2e