The card reader for the Inspiron 14 7447 is much the same as others in the Dell range such as the Vostro 5480 as well as the Inspiron 7548 card reader hardware. There are a number of versions of the hardware however all four versions use the same card reader driver. You can download the driver below as well as check the hardware which will make use of this software driver.
Inspiron 14 7447 : Realtek RTS5227E Card Reader Driver
The following hardware makes use of this driver. Note that this driver was last updated in 2015 when the hardware was released. This is a Windows 10 driver for both 32bit as well as for 64bit operating systems. Check your hardware as well as software versions. This is Version 10.0.370.88, A00 of the card reader driver for the Inspiron 14 7447.