What is the issue with applying the Laplace transform to tcos(4t)?

[Feodalherren]

Homework Statement

f(t)=tcos(4t)

Homework Equations

tⁿf(t)=(-1)ⁿ dF(s)/dsⁿ

The Attempt at a Solution

I don't understand why this formula is giving me the oppiste sign of the answer.

If I apply the formula I get

(16-s²)/(s²+16)²

Because n=1 I need to multiply by a negative but this yields the incorrect answer.

 

[leafjerky]

Yours looks different than the one we use. Try it as:

 

[LCKurtz]

Homework Statement

f(t)=tcos(4t)

Homework Equations

tⁿf(t)=(-1)ⁿ dF(s)/dsⁿ

The Attempt at a Solution

I don't understand why this formula is giving me the oppiste sign of the answer.

If I apply the formula I get

(16-s²)/(s²+16)²

Because n=1 I need to multiply by a negative but this yields the incorrect answer.

$$-\frac{-s^2+16}{(s^2+16)^2}=\frac{s^2-16}{(s^2+16)^2}$$which is correct.

 

[leafjerky]

His answer doesn't have a negative in front?
Edit: nevermind, looking at wrong thing. Carry on

 

[Feodalherren]

But that's not what I'm getting.

Taking the derivative of s/(s²+16)

= (s(2s)-(s²+16)/(s²+16)²

now multiply the result with -1 and we get the opposite sign for the answer.

 

[LCKurtz]

But that's not what I'm getting.

Taking the derivative of s/(s²+16)

= (s(2s)-(s²+16)/(s²+16)²

now multiply the result with -1 and we get the opposite sign for the answer.

That is because your quotient rule is wrong.

 

[Feodalherren]

Ah I see. Thank you!