Prove this property of convolution. d/dt y(t) = x(t) * [d/dt h(t)] and d/dt y(t) = [d/dx x(t)] * h(t)

Question

I've tried solving for the first one: d/dt y(t) = x(t) * [d/dt h(t)] This is as far as I've gotten. integral from -inf to inf (x(tau) * d/dt h(t-tau) dtau) not sure how to go from here.

d/dt y(t) = [d/dx x(t)] * h(t)