How Can I Prove y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t)?

[benfrankballi]

how would I show that y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t)

I know that in an LTI system y(t) = x(t) * h(t) = $\int$ x($\tau$) * h(t-$\tau$) from $\infty$ to -$\infty$

But how would I go about trying to prove the first two equations?

 

[jackmell]

Why not just differentiate the convolution integral:

$$\frac{d}{dt}\int_{-\infty}^{\infty} x(\tau) h(t-\tau)d\tau=\int_{-\infty}^{\infty} x(\tau)h'(t-\tau)d\tau=x(t)*h'(t)$$