If `5f(x)+3f(1/x)=x+2` and `y=x f(x),` then find `dy/dx` at `x=1`.

If f'(x)=x/2 + 2/x and f(1)=5/4 , then find f(x) .

If f'(x)= sqrt(2x^(2)-1) and y=f(x^(2)),then (dy)/(dx) at x = 1 is

If y=f((2x-1)/(x^2+1)) and f^'(x)=sinx^2 , then find (dy)/(dx)

If y = f (log_e x) and f'(2) = 2 , find dy/dx at x = e^2

If f^2(x)*f((1-x)/(1+x))=x^3, [x!=-1,1 and f(x)!=0], then find |[f(-2)]| (where [] is the greatest integer function).

If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1 , then find the value of lim_(x->0)(2^(f(tan x)-2^f(sin x)))/(x^2*f(sin x))

If f(x) =3x^4-5x^2+7 , find f(x-1).

If f(x) = 3x^2+5x-1 , find f’.

If f'(x)=x^2-1/x^2 and f(1)=1/3 , find f(x).

Find dy/dx if f(x)=x^2e^x