Derivative of sinc(x) and Finding y(t): Step-by-Step Solution

[krispots]

Homework Statement

find y(t) = d(x(t))/dt

where x(t) = 23sin(at)/(at)

where a = 147*pi*2

Homework Equations

The Attempt at a Solution

y(t) = 23/a * [ (t^-1) * sin(at) ]
= 23/a * [ -(t^-2) * sin(at) + (t^-1) * a * cos(at) ]

is this correct? my derivatives are old and rusty.

 

[HallsofIvy]

Homework Statement

find y(t) = d(x(t))/dt

where x(t) = 23sin(at)/(at)

where a = 147*pi*2

Homework Equations

The Attempt at a Solution

y(t) = 23/a * [ (t^-1) * sin(at) ]
= 23/a * [ -(t^-2) * sin(at) + (t^-1) * a * cos(at) ]

is this correct? my derivatives are old and rusty.

First, don't write "= " between different things. y= the first line but not the second. Yes,
y'= (23/a)[-(t^-2 sin(at)+ t^-1 a cos(at)]