What is the derivative of a unit step function with discontinuities at -2 and 2?

In summary, the conversation is discussing the validity of the equation d/dt {(u(-2-t) + u(t-2)} = q(-2-t) + q(t-2) and whether it should have a negative sign in front of the first q term. The conversation also mentions the function u(t) and its continuity at t=0.
  • #1
ColdStart
19
0
ok letsa say i have d/dt {(u(-2-t) + u(t-2)}

I know that d/dt { u(t) } is q(t)...

now is it correct to think that d/dt {(u(-2-t) + u(t-2)} = q(-2-t) + q(t-2) ?
 
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  • #2
HI ColdStart! :wink:
ColdStart said:
ok letsa say i have d/dt {(u(-2-t) + u(t-2)}

I know that d/dt { u(t) } is q(t)...

now is it correct to think that d/dt {(u(-2-t) + u(t-2)} = q(-2-t) + q(t-2) ?

Nope … try again, using the chain rule (with g = -2-t) …

what do you get? :smile:
 
  • #3
ok so:
d/dt {(u(-2-t) + u(t-2)} = d/dt{ u(-(t+2)) + u(t-2)} = -q(t+2) + q(t-2) ?
 
  • #4
ColdStart said:
ok so:
d/dt {(u(-2-t) + u(t-2)} = d/dt{ u(-(t+2)) + u(t-2)} = -q(t+2) + q(t-2) ?

Yes :smile:, except it should still be -(t+2) inside the first q, shouldn't it? :wink:
 
  • #5
well then it turns out that its what i wrote in my first post, but in one book it shows -q(t+2)... that's why i got confused and was asking it here..
 
  • #6
ColdStart said:
well then it turns out that its what i wrote in my first post, but in one book it shows -q(t+2)... that's why i got confused and was asking it here..

No, in your first post you had …
ColdStart said:
q(-2-t) + q(t-2) ?

with no minus in front of the q.

(the book result would be the same if q is an odd function)
 
  • #7
cool thanks!
 
  • #8
Is [tex]\frac{du}{dt}=\delta (t)[/tex] valid for all t?

But the function u(t) is not continuous at t=0. :confused:
 

What is the derivative of a unit step function?

The derivative of a unit step function, also known as the Heaviside step function, is equal to zero everywhere except at the discontinuity point, where it is undefined.

How do you find the derivative of a unit step function?

To find the derivative of a unit step function, you can use the limit definition of a derivative. Take the limit as the input approaches the discontinuity point, and the result will be the value of the derivative at that point.

What is the graphical representation of the derivative of a unit step function?

The derivative of a unit step function is a straight line with a slope of zero everywhere except at the discontinuity point, where it is undefined. This can be visualized on a graph as a horizontal line with a vertical jump at the discontinuity point.

Is the derivative of a unit step function continuous?

No, the derivative of a unit step function is not continuous. It is defined and equal to zero everywhere except at the discontinuity point, where it is undefined.

What is the physical significance of the derivative of a unit step function?

The derivative of a unit step function represents the rate of change of the function at the discontinuity point. In other words, it shows how quickly the function is increasing or decreasing at that point.

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