7.If `f(x)=1+x+x^(2)+.........` then find f'(x) .

If f(x)=A x^2+B x+C then find f '(x)

Let f (x) = x tan ^(-1) (x^(2)) then find the f'(x)

If f(x)=(x-4)/(2sqrt(x)) , then find f'(1)

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

Let f:DtoR , where D is the domain of f . Find the inverse of f if it exists: Let f:[0,3]to[1,13] is defined by f(x)=x^(2)+x+1 , then find f^(-1)(x) .

If f(x)=(x-|x|)/(|x|) , then find f(-1).

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

If f_1(x)=(1)/(x), f_(2) (x)=1-x, f_(3) (x)=1/(1-x) then find J(x) such that f_(2) o J o f_(1) (x)=f_(3) (x) (a) f_(1) (x) (b) (1)/(x) f_(3) (x) (c) f_(3) (x) (d) f_(2) (x)

If f(x)=x^2+x+1 , then find the value of 'x' for which f(x-1) =f(x)

If f'(x) = 1/x + x^2 and f(1)=4/3 then find the value of f(x)