Chapter 12, Problem 22P

(a)

To determine

Determine the Laplace transform of $\frac{d}{dt}\sin \omega t$.

(b)

To determine

Determine the Laplace transform of $\frac{d}{dt}\cos \omega t$.

(c)

To determine

Determine the Laplace transform of $\frac{d^3}{d{t}^3}\left(t^2\right)u\left(t\right)$.

(d)

To determine

Verify the answers in Part (a), Part (b) and Part (c) by differentiating the function first and then obtaining the Laplace transform.