Question

a communication signal is given by the function y=sint/t
derive and equation for dy/dt using the quotient rule.

Answer 1

Quotient rule:

$d\left(\frac{u}{v}\right)=\frac{v\cdot du-u\cdot dv}{v^2}$

Given function

$y=\frac{sint}{t}$

Differentiating with respect to t using quotient rule

$\frac{dy}{dt}=\frac{t\cdot \frac{d}{dt}\left(sint\right)-sint\cdot \frac{d}{dt}\left(t\right)}{t^2}$

we know $\frac{d}{dt}\left(sint\right)=cost\:\:and\:\frac{d}{dt}\left(t\right)=1$

$\frac{dy}{dt}=\frac{t\cdot cost-sint\cdot 1}{t^2}$

$\frac{dy}{dt}=\frac{t\cdot cost-sint}{t^2}$