If f(t) =t^4 -2t^2+3t,

Question

find f'(t) and f"(t)

Answer 1

f(t) = t^4-2t^2+3t

Apply derivative with respect to t each side.

f^'(t)  = d/dt(t^4-2t^2+3t)                                                       Recall the formulae

      = d/dt(t^4)-d/dt(2t^2)+d/dt(3t)                                        d/dx(xⁿ) = nx^n-1

      = 4t^3-4t+3                                                                    d/dx(x) = 1

Apply derivative with respect of t to each side.                 d/dx(constant) =0

f^"(t) = d/dt(4t^3-4t+3)

      = d/dt (4t^3)-d/dt(4t)+d/dt(3)

     = 12t^2-4