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

If f is a differentiable function of x such that f(1)=0,f'(1)=(3)/(5)" and "y=e^(x)*f(e^(2x))," then the value of "(dy)/(dx)" at "x=0 is

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)

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)=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 y=f{f(x)} , f(0) =0 and f'(0)=5, then the value of [(dy)/(dx)]_(x=0) is-

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 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

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0), then the value of k is