# Laplace transform tcos(4t)

1. May 6, 2015

### Feodalherren

1. The problem statement, all variables and given/known data
f(t)=tcos(4t)

2. Relevant equations

tnf(t)=(-1)n dF(s)/dsn

3. 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.

2. May 6, 2015

### leafjerky

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

3. May 6, 2015

### LCKurtz

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

4. May 6, 2015

### leafjerky

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

5. May 6, 2015

### 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.

6. May 7, 2015

### LCKurtz

That is because your quotient rule is wrong.

7. May 7, 2015

### Feodalherren

Ah I see. Thank you!