I had this same problem, Win10, IOS 9.0.1, IPhone6, and Upgraded Itunes 12.3.0.44 and it would not recognize my IPhone6 was connected, but forcing a reinstall of the Apple IPhone Device Driver for the IPhone worked; follow these steps:
If anyone else has this problem with 12.3.0.44 and Windows 10, I fixed it by following these steps.
In Windows Device Manager look for your Apple IPhone; probably located under Portable Devices
Right-click the Apple iPhone, Apple iPad, or Apple iPod entry in Device Manager and choose Update Driver from the shortcut menu.
Click "Browse my computer for driver software".
Click "Let me pick from a list of device drivers on my computer".
Click the Have Disk button.
(If the Have Disk option is not present, choose a device category such as Mobile Phone or Storage Device if listed, and click next. The Have Disk button should then appear.)
In the "Install from Disk" dialog, click the Browse button.
Use this window to navigate to the following folder:
C:\Program Files\Common Files\Apple\Mobile Device Support\Drivers.
Double-click the "usbaapl" file. (This file will be called "usbaapl64" if you have a 64-bit version of Windows. If you don't see "usbaapl64" here, or if there is no Drivers folder, look in C:\Program Files (x86)\Common Files\Apple\Mobile Device Support\Drivers. instead).
Click OK in the "Install from Disk" dialog.
Click Next and finish the driver-installation steps. Open iTunes to verify that the device is recognized properly.
This fixed my problem immediately. Good Luck.