The degree of (projectively) dual variety

Question

Let $X\subset \mathbb P^n$ be a (smooth) hypersurface of degree $d$ (over $\mathbb C$). Let $X^*\subset \mathbb P^{n*}$ be the dual variety (in the senese that all hyperplanes tangent to $X$, together with the natural scheme structure). How can we compute the degree of $X^*$?