# Laplace transform of convolution with derivative in it

1. Oct 9, 2011

### tjosan

1. The problem statement, all variables and given/known data

Hi,

I am wondering how to Laplace transform this expression

$$f(t)=\int^{\tau}_{0} g(\tau)f'(t-\tau)d\tau$$
or more precisely
$$f(t)=\int^{\tau}_{0} sin(8\tau)f'(t-\tau)d\tau$$

The $$f'(t-\tau)$$ gets me confused.

2. Relevant equations

$$\int^{\tau}_{0} f(t-\tau)g(\tau)d\tau$$
and the laplace transform of that is:
$$F(s)G(s)$$

3. The attempt at a solution
I have no idea how to proceed.

Maybe
$$F(s)=8/(s^2+8^2)(sF(s)-f(0))$$

Last edited: Oct 9, 2011
2. Oct 9, 2011