Multiple choice

The unilateral Laplace transform of f(t) is $\dfrac{1}{s^2 + s +1}$. The unilateral Laplace transform of t f (t) is

  1. - $\dfrac{1}{ (s^2 + s +1)^2}$
  2. - $\dfrac{2s+1}{ (s^2 + s +1)^2}$
  3. $\dfrac{s}{ (s^2 + s +1)^2}$
  4. $\dfrac{2s+1}{ (s^2 + s +1)^2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Laplace transform property states L{tf(t)} = -d/ds[F(s)]. Differentiating F(s) = (s²+s+1)^(-1) gives dF/ds = -(2s+1)(s²+s+1)^(-2), so L{tf(t)} = (2s+1)/(s²+s+1)².