Can't bind to 'matDatepicker' since it isn't a known property of 'input' - Angular

While using mat-datepicker, you have to import MatDatepickerModule as well, also MatNativeDateModule is recommended to be imported too. see docs here.

import { MaterialModule, MatDatepickerModule, MatNativeDateModule } from '@angular/material';
@NgModule({
  imports: [
    ...
    MaterialModule,            // <----- this module will be deprecated in the future version.
    MatDatepickerModule,        // <----- import(must)
    MatNativeDateModule,        // <----- import for date formating(optional)
    MatMomentDateModule         // <----- import for date formating adapted to more locales(optional)
  ]

For optional module of date formating, see Module for DateAdapter from material team.

Mention: please avoid using MaterialModule for it'll be deprecated in the future.

you need to import FormsModule and ReactiveFormsModule if you used NgModule and formgroup. so your app.module should be like that

import {MaterialModule} from '@angular/material';
@NgModule({
  imports: [
    MdDatepickerModule,        
    MdNativeDateModule,
    FormsModule,
    ReactiveFormsModule
  ]

Note: MaterialModule Removed. please use separate module instead. like MdDatepickerModule see here https://github.com/angular/material2/blob/master/CHANGELOG.md#200-beta11-carapace-parapet-2017-09-21