HD Laptop and adding external 4k monitor - not getting 60hz

[maverick22]

So, my wife's Dell XPS 13" laptop is about 4 years old or so. My wife wants a bigger monitor since she will be home for much of the school year, so I let her have my 32" 4k monitor. I have tried both miniDisplay to HDMI and miniDisplay to DisplayPort.

I can get the laptop monitor and the 4k monitor to both be used at the same time as this is what my wife wants. We are using the "extend displays" feature.

However, I can only get the following:

1) the 4k monitor actually displaying in 4k at 30hz, causing mouse lag and overall slowness in web page loading and basically everything

2) the 4k monitor displaying 1920 x 1080p at 60hz, which is much smoother, and everything runs as it should (text and icons are slightly pixelated though, defeating the purpose of the 4k monitor)

I cannot get the best of both worlds: 4k displayed WITH 60hz.

Any ideas?

Thank you in advance!