Answer to Question #114408 in Calculus for Josh Miles

Question

A communication signal is given by the function =sin⁡t/t . Derive an equation for dy/dt using the Quotient Rule.

Answer 1

Quotient Rule: $(\frac{u}{v})'=\frac{u'v-uv'}{v^2}$

$y=\frac{sin(t)}{t}$

here $u=sin(t)$ and $v=t$

$u'=\frac{du}{dt}=cos(t)$

$v'=\frac{dv}{dt}=1$

So, $\frac{dy}{dt}=\frac{cos(t)\cdot t-sin(t)\cdot 1}{t^2}=\frac{t\cdot cos(t)-sin(t)}{t^2}$