If `f(0)=0,f^(prime)(0)=2,` then the derivative of `y=f(f(f(x)))` at `x=0` is 2 (b) 8 (c) 16 (d) 4

If f(1)=4 , f^(prime)(1)=2 , find the value of the derivative of log(f(e^x)) with respect to x at the point x=0 .

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

Consider the function f(x)={xsinpi/x ,forx >0 0,forx=0 The, the number of point in (0,1) where the derivative f^(prime)(x) vanishes is 0 (b) 1 (c) 2 (d) infinite

Let f(0)=f'(0)=0 and f^(primeprime)(x)=sec^4x+4 then find f(x)

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 .

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) is differentiable and strictly increasing function, then the value of ("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0)) is 1 (b) 0 (c) -1 (d) 2

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: RvecR be such that f(a)=1,f^(prime)(a)=2. Then (lim)_(xvec0)((f^2(a+x))/(f(a)))^(1//x) is a. e^2 b. e^4 c. e^(-4) d. 1//e

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these