# Convolution Integral Properties

by benfrankballi
Tags: convolution, integral, properties
 P: 2 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?
 P: 1,666 Why not just differentiate the convolution integral: $$\frac{d}{dt}\int_{-\infty}^{\infty} x(\tau) h(t-\tau)d\tau=\int_{-\infty}^{\infty} x(\tau)h'(t-\tau)d\tau=x(t)*h'(t)$$

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