We address global sensitivity analysis for models with high-dimensional inputs and function-valued (functional) outputs. Variance-based global sensitivity approaches based on Sobol’ indices have been proven useful in a wide range of outputs. However, Sobol’ indices can be challenging to compute for computationally intensive models with a large number of parameters. We propose derivative based global sensitivity measures (DGSMs) for models with functional outputs, and derive a link between these functional DGSMs and generalized Sobol’ indices for functional outputs. The functional DGSMs are typically much more efficient to compute in practice. We present illustrative numerical results for an epidemic cholera described by nonlinear system of ordinary differential equations.