Laplace differentiation question

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SUMMARY

The discussion focuses on the application of the Laplace transform, specifically the differentiation process involved when multiplying a function by 't' or 't^n'. The key formula discussed is L{tf(t)} = -F'(s), with an example provided: L{sin(2t)} = 2 / (s^2 + 4) leading to L{tsin(2t)} = -d/ds(2 / (s^2 + 4)) = 4s / (s^2 + 4)^2. The confusion arises from the differentiation step, which involves applying the quotient rule to differentiate the function.

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  • Understanding of Laplace transforms
  • Familiarity with differentiation techniques, particularly the quotient rule
  • Basic knowledge of trigonometric functions, specifically sine
  • Proficiency in algebraic manipulation of rational functions
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  • Learn about the applications of Laplace transforms in solving differential equations
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kris
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Hi I'm learning laplace transform, specifically multiplying by 't' and 't^n'. Now i understand the concept that L{tf(t)} = -F'(s) but I'm confused with the differentiation part of the process (having a bit of a dim moment!).

Here is the example it gives:

L{sin2t} = 2 / (s^2 + 4), therefore L{tsin2t} = -d/ds(2 / (s^2 +4)) = 4s / (s^2 + 4)^2

the differentiation at the end is the bit that is confusing me i.e. how to do it. I know this should be the simple bit but it completely evades my understanding at this point :smile:.

Any help would be appreciated

thanks
 
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I'll assume you know how to differentiate. Let u=s2+4.
d/ds(2/u)=-(2/u2)du/ds. du/ds=2s. Just put it all together.
 

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