  We develop a general approach to estimating the derivative of a
function-valued parameter $\theta_o(u)$ that is identified for every value of
$u$ as the solution to a moment condition. This setup in particular covers many
interesting models for conditional distributions, such as quantile regression
or distribution regression. Exploiting that $\theta_o(u)$ solves a moment
condition, we obtain an explicit expression for its derivative from the
Implicit Function Theorem, and estimate the components of this expression by
suitable sample analogues, which requires the use of (local linear) smoothing.
Our estimator can then be used for a variety of purposes, including the
estimation of conditional density functions, quantile partial effects, and
structural auction models in economics.
