Let $X \subset \mathbb{A}^{n}$ be an affine variety then we know that the dimension of $T_{p}(X)$ the tangent space of $X$ at a point $p$ is equal to $n$ minus the rank of the Jacobian (at p)
Is this true if $X$ is a projective variety? or at least $X=Z(f)$ where $f$ is a homogeneous polynomial? In case this is not true, what is the method to compute the dimension of the tangent space of a projective variety?