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

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The discussion focuses on finding the derivative of the function x(t) = 23sin(at)/(at), where a = 147π2. The correct derivative, y(t), is established as y' = (23/a)[-(t^-2)sin(at) + (t^-1)a cos(at)]. Participants confirm the accuracy of the derivative and provide feedback on notation, emphasizing the importance of clarity in mathematical expressions.

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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.
 
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krispots said:

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)]
 

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